Selected publications

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• D. Vollhardt, K. Byczuk, and M. Kollar,
  Dynamical Mean-Field Theory,  
  in: Strongly Correlated Systems, ed. by A. Avella and F. Mancini, Springer Series in Solid-State Sciences (Springer Berlin Heidelberg, 2011), Vol. 171, p. 203-236
  [arXiv:1109.4833].
  

  The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.

• M. Kollar,
  Dynamical mean-field theory,  
  in: The LDA+DMFT approach to strongly correlated materials,
  ed. by E. Pavarini, E. Koch, D. Vollhardt, and A. I. Lichtenstein, Chapter 5 (Forschungszentrum Jülich, 2011)
  [PDF at fz-juelich.de].
  
  
• P. van Dongen, M. Kollar, and T. Pruschke (eds.),
  Electronic Correlations in Models and Materials (Special Topic Issue),  
  Ann. Phys. 523 (8-9), 583-758 (2011).
  Preface.
  
  
• M. Kollar, F. A. Wolf, and M. Eckstein,
  Generalized Gibbs ensemble prediction of prethermalization plateaus and their relation to nonthermal steady states in integrable systems,  
  Phys. Rev. B 84, 054304 (2011) [ PDF / AIP 2011 ].
  Selected for PRB Editors' Suggestions.
  [arXiv:1102.2117]
  

  A quantum many-body system which is prepared in the ground state of an integrable Hamiltonian does not directly thermalize after a sudden small parameter quench away from integrability. Rather, it will be trapped in a prethermalized state and can thermalize only at a later stage. We discuss several examples for which this prethermalized state shares some properties with the nonthermal steady state that emerges in the corresponding integrable system. These examples support the notion that nonthermal steady states in integrable systems may be viewed as prethermalized states that never decay further. Furthermore we show that prethermalization plateaus are under certain conditions correctly predicted by generalized Gibbs ensembles, which are the appropriate extension of standard statistical mechanics in the presence of many constants of motion. This establishes that the relaxation behaviors of integrable and nearly integrable systems are continuously connected and described by the same statistical theory.

• A. P. Kampf, M. Kollar, J. Kuneš, M. Sentef, and D. Vollhardt,
  Material-Specific Investigations of Correlated Electron Systems,
  in: High Performance Computing in Science and Engineering, Garching/Munich 2009, ed. by S. Wagner, M. Steinmetz, A. Bode and M. M. Müller (Springer, Heidelberg, 2010), pp. 599-612.
  [arXiv:0910.5126]
  

  We present the results of numerical studies for selected materials with strongly correlated electrons using a combination of the local-density approximation and dynamical mean-field theory (DMFT). For the solution of the DMFT equations a continuous-time quantum Monte-Carlo algorithm was employed. All simulations were performed on the supercomputer HLRB II at the Leibniz Rechenzentrum in Munich. Specifically we have analyzed the pressure induced metal-insulator transitions in Fe₂O₃ and NiS₂, the charge susceptibility of the fluctuating-valence elemental metal Yb, and the spectral properties of a covalent band-insulator model which includes local electronic correlations.

• M. Eckstein, A. Hackl, S. Kehrein, M. Kollar, M. Moeckel, P. Werner, and F. A. Wolf,
  New theoretical approaches for correlated systems in nonequilibrium,
  Eur. Phys. J. Special Topics 180, 217 (2010).
  Volume on Cooperative Phenomena in Solids with Electronic Correlations [Editorial].
  [arXiv:1005.5097]
  

  We review recent developments in the theory of interacting quantum many-particle systems that are not in equilibrium. We focus mainly on the nonequilibrium generalizations of the flow equation approach and of dynamical mean-field theory (DMFT). In the nonequilibrium flow equation approach one first diagonalizes the Hamiltonian iteratively, performs the time evolution in this diagonal basis, and then transforms back to the original basis, thereby avoiding a direct perturbation expansion with errors that grow linearly in time. In nonequilibrium DMFT, on the other hand, the Hubbard model can be mapped onto a time-dependent self-consistent single-site problem. We discuss results from the flow equation approach for nonlinear transport in the Kondo model, and further applications of this method to the relaxation behavior in the ferromagnetic Kondo model and the Hubbard model after an interaction quench. For the interaction quench in the Hubbard model, we have also obtained numerical DMFT results using quantum Monte Carlo simulations. In agreement with the flow equation approach they show that for weak coupling the system relaxes to a "prethermalized" intermediate state instead of rapid thermalization. We discuss the description of nonthermal steady states with generalized Gibbs ensembles.

• J. Kuneš, I. Leonov, M. Kollar, K. Byczuk, V. I. Anisimov, and D. Vollhardt,
  Dynamical mean-field approach to materials with strong electronic correlations,
  Eur. Phys. J. Special Topics 180, 5 (2010).
  Volume on Cooperative Phenomena in Solids with Electronic Correlations [Editorial].
  [arXiv:1003.3600]
  

  We review recent results on the properties of materials with correlated electrons obtained within the LDA+DMFT approach, a combination of a conventional band structure approach based on the local density approximation (LDA) and the dynamical mean-field theory (DMFT). The application to four outstanding problems in this field is discussed: (i) we compute the full valence band structure of the charge-transfer insulator NiO by explicitly including the p-d hybridization, (ii) we explain the origin for the simultaneously occuring metal-insulator transition and collapse of the magnetic moment in MnO and Fe₂O₃, (iii) we describe a novel GGA+DMFT scheme in terms of plane-wave pseudopotentials which allows us to compute the orbital order and cooperative Jahn-Teller distortion in KCuF₃ and LaMnO₃, and (iv) we provide a general explanation for the appearance of kinks in the effective dispersion of correlated electrons in systems with a pronounced three-peak spectral function without having to resort to the coupling of electrons to bosonic excitations. These results provide a considerable progress in the fully microscopic investigations of correlated electron materials.

• M. Eckstein and M. Kollar,
  Near-adiabatic parameter changes in correlated systems: influence of the ramp protocol on the excitation energy,
  New J. Phys.12, 055012 (2010) [ PDF / IOP+DPG 2010 ].
  Focus on Dynamics and Thermalization in Isolated Quantum Many-Body Systems [Editorial].
  [arXiv:0911.1282]
  

  We study the excitation energy for slow changes of the hopping parameter in the Falicov-Kimball model with nonequilibrium dynamical mean-field theory. The excitation energy vanishes algebraically for long ramp times with an exponent that depends on whether the ramp takes place within the metallic phase, within the insulating phase, or across the Mott transition line. For ramps within metallic or insulating phase the exponents are in agreement with a perturbative analysis for small ramps. The perturbative expression quite generally shows that the exponent depends explicitly on the spectrum of the system in the initial state and on the smoothness of the ramp protocol. This explains the qualitatively different behavior of gapless (e.g., metallic) and gapped (e.g., Mott insulating) systems. For gapped systems the asymptotic behavior of the excitation energy depends only on the ramp protocol and its decay becomes faster for smoother ramps. For gapless systems and sufficiently smooth ramps the asymptotics are ramp-independent and depend only on the intrinsic spectrum of the system. However, the intrinsic behavior is unobservable if the ramp is not smooth enough. This is relevant for ramps to small interaction in the fermionic Hubbard model, where the intrinsic cubic fall-off of the excitation energy cannot be observed for a linear ramp due to its kinks at the beginning and the end.

• M. Eckstein, M. Kollar, and P. Werner,
  Interaction quench in the Hubbard model: Relaxation of the spectral function and the optical conductivity,
  Phys. Rev. B 81, 115131 (2010) [ PDF / AIP 2010 ].
  [arXiv:0910.5674]
  

  We use non-equilibrium dynamical mean-field theory in combination with a recently developed Quantum Monte Carlo impurity solver to study the real-time dynamics of a Hubbard model which is driven out of equilibrium by a sudden increase in the on-site repulsion U. We discuss the implementation of the self-consistency procedure and some important technical improvements of the QMC method. The exact numerical solution is compared to iterated perturbation theory, which is found to produce accurate results only for weak interaction or short times. Furthermore we calculate the spectral functions and the optical conductivity from a Fourier transform on the finite Keldysh contour, for which the numerically accessible timescales allow to resolve the formation of Hubbard bands and a gap in the strongly interacting regime. The spectral function, and all one-particle quantities that can be calculated from it, thermalize rapidly at the transition between qualitatively different weak- and strong-coupling relaxation regimes.

• M. Eckstein, M. Kollar, and P. Werner,
  Thermalization after an interaction quench in the Hubbard model,
  Phys. Rev. Lett. 103, 056403 (2009) [ PDF / AIP 2009 ].
  Selected for vjaqf.org: Virtual Journal of Atomic Quantum Fluids 1/2 (2009).
  [arXiv:0904.0976]
  

  We use nonequilibrium dynamical mean-field theory to study the time evolution of the fermionic Hubbard model after an interaction quench. Both in the weak-coupling and in the strong-coupling regime the system is trapped in quasistationary states on intermediate time scales. These two regimes are separated by a sharp crossover at U_c^dyn=0.8 in units of the bandwidth, where fast thermalization occurs. Our results indicate a dynamical phase transition which should be observable in experiments on trapped fermionic atoms.

• M. Eckstein and M. Kollar,
  Measuring correlated electron dynamics with time-resolved photoemission spectroscopy,
  Phys. Rev. B 78, 245113 (2008) [ PDF / AIP 2008 ].
  [arXiv:0809.4282]
  

  Time-resolved photoemission experiments can reveal fascinating quantum dynamics of correlated electrons. However, the thermalization of the electronic system is typically so fast that very short probe pulses are necessary to resolve the time evolution of the quantum state, and this leads to poor energy resolution due to the energy-time uncertainty relation. Although the photoemission intensity can be calculated from the nonequilibrium electronic Green functions, the converse procedure is therefore difficult. We analyze a hypothetical time-resolved photoemission experiment on a correlated electronic system, described by the Falicov-Kimball model in dynamical mean-field theory, which relaxes between metallic and insulating phases. We find that the real-time Green function which describes the transient behavior during the buildup of the metallic state cannot be determined directly from the photoemission signal. On the other hand, the characteristic collapse-and-revival oscillations of an excited Mott insulator can be observed as oscillating weight in the center of the Mott gap in the time-dependent photoemission spectrum.

• M. Eckstein and M. Kollar,
  Theory of time-resolved optical spectroscopy on correlated electron systems,
  Phys. Rev. B 78, 205119 (2008) [ PDF / AIP 2008 ].
  Selected for PRB Editors' Suggestions.
  Selected for vjultrafast.org: Virtual Journal of Ultrafast Science 7/12 (2008).
  [arXiv:0808.1005]
  

  The real-time dynamics of interacting electrons out of equilibrium contains detailed microscopic information about electronically correlated materials, which can be read out with time-resolved optical spectroscopy. The reflectivity that is typically measured in pump-probe experiments is related to the nonequilibrium optical conductivity. We show how to express this quantity in terms of real-time Green functions using dynamical mean-field theory. As an application we study the electrical response of the Falicov-Kimball model during the ultrafast buildup of the gapped phase at large interaction.

• M. Kollar and M. Eckstein,
  Relaxation of a one-dimensional Mott insulator after an interaction quench,
  Phys. Rev. A 78, 013626 (2008) [ PDF / AIP 2008 ].
  [arXiv:0804.2254]
  

  We obtain the exact time evolution for the one-dimensional integrable fermionic 1/r Hubbard model after a sudden change of its interaction parameter, starting from either a metallic or a Mott-insulating eigenstate. In all cases the system relaxes to a new steady state, showing that the presence of the Mott gap does not inhibit relaxation. The properties of the final state are described by a generalized Gibbs ensemble. We discuss under which conditions such ensembles provide the correct statistical description of isolated integrable systems in general. We find that generalized Gibbs ensembles do predict the properties of the steady state correctly, provided that the observables or initial states are sufficiently uncorrelated in terms of the constants of motion.

• M. Eckstein and M. Kollar,
  Nonthermal steady states after an interaction quench in the Falicov-Kimball model,
  Phys. Rev. Lett. 100, 120404 (2008) [ PDF / AIP 2008 ].
  [arXiv:0707.2789]
  

  We present the exact solution of the Falicov-Kimball model after a sudden change of its interaction parameter using dynamical mean-field theory. For different interaction quenches between the homogeneous metallic and insulating phases the system relaxes to a non-thermal steady state on time scales on the order of hbar/bandwidth, showing collapse and revival with an approximate period of h/interaction if the interaction is large. We discuss the reasons for this behavior and provide a statistical description of the final steady state by means of generalized Gibbs ensembles.

• L. Zherlitsyna, N. Auner, M. Bolte, Y. Pozdniakova, O. Shchegolikhina, K. Lyssenko, V. Pashchenko, B. Wolf, M. Lang, F. Schütz, M. Kollar, F. Sauli, and P. Kopietz,
  Synthesis, Structure and Magnetic Properties of a Novel Hexanuclear Copper Methylsiloxane Complex,
  Eur. J. Inorg. Chem. 30, 4827 (2007).
  

  A new hexanuclear copper(II) sandwich complex based on two 12-membered macrocyclic methylsiloxanolate ligands, Cu₆[(MeSiO₂)₆]₂·6DMF, was synthesized and characterized by single crystal X-ray diffraction analysis and magnetic measurements. The cluster compound crystallizes in the monoclinic system, space group P21/n (No.14), with a=13.3728(5)Å, b=15.4281(7)Å, c=17.4335(7)Å, β=98.932(3)° and Z=2. The unit cell contains two identical macromolecules, each consisting of six interacting Cu²⁺ (S=1/2) ions. Within the macromolecule the six oxygen-bridged Cu²⁺ ions are arranged into an almost regular hexagon. An analysis of the high-temperature part of the magnetic susceptibility reveals that the complex has a strong average ferromagnetic Cu-Cu exchange interaction of J_av/k_B=50.4±1K with a high-spin S=3 ground state. A satisfactory fit for the magnetic susceptibility and the magnetization in the whole accessible temperature range is obtained from a Heisenberg model with nonuniform exchange couplings within a ring, corresponding to a system of two weakly coupled trimers with a ferromagnetic intratrimer exchange coupling of J/k_B=72.5 K and a ferromagnetic intertrimer exchange coupling of J'/k_B=7K.

• M. Sentef, M. Kollar, and A. P. Kampf,
  Spin transport in Heisenberg antiferromagnets in two and three dimensions,
  Phys. Rev. B 75, 214403 (2007) [ PDF / AIP 2007 ].
  Selected for vjnano.org: Virtual Journal of Nanoscale Science & Technology 15/24 (2007).
  [cond-mat/0612215]
  

  We analyze spin transport in insulating antiferromagnets described by the XXZ Heisenberg model in two and three dimensions. Spin currents can be generated by a magnetic-field gradient or, in systems with spin-orbit coupling, perpendicular to a time-dependent electric field. The Kubo formula for the longitudinal spin conductivity is derived analogously to the Kubo formula for the optical conductivity of electronic systems. The spin conductivity is calculated within interacting spin-wave theory. In the Ising regime, the XXZ magnet is a spin insulator. For the isotropic Heisenberg model, the dimensionality of the system plays a crucial role: In d=3 the regular part of the spin conductivity vanishes linearly in the zero frequency limit, whereas in d=2 it approaches a finite zero frequency value.

• K. Byczuk, W. Hofstetter, M. Kollar, and D. Vollhardt,
  Surprises in Correlated Electron Physics,
  Acta Phys. Pol. A 111, 549 (2007).
  

  Strong electronic correlations and especially the interplay between correlations and disorder lead to many interesting and quite unexpected phenomena. A short summary of our recent investigations into the properties of strongly correlated electron systems with and without disorder using the dynamical mean-field theory is presented.

• M. Eckstein, M. Kollar, and D. Vollhardt,
  Isosbestic points in the spectral function of correlated electrons,
  J. Low Temp. Phys.147, 279 (2007).
  [cond-mat/0609464]
  

  We investigate the properties of the spectral function A(&omega,U) of correlated electrons within the Hubbard model and dynamical mean-field theory. Curves of A(&omega,U) vs. &omega for different values of the interaction U are found to intersect near the band-edges of the non-interacting system. For a wide range of U the crossing points are located within a sharply confined region. The precise location of these 'isosbestic points' depends on details of the non-interacting band structure. Isosbestic points of dynamic quantities therefore provide valuable insights into microscopic energy scales of correlated systems.

• M. Eckstein, M. Kollar, M. Potthoff, and D. Vollhardt,
  Phase separation in the particle-hole asymmetric Hubbard model,
  Phys. Rev. B 75, 125103 (2007) [ PDF / AIP 2007 ].
  [cond-mat/0610803]
  

  The paramagnetic phase diagram of the Hubbard model with nearest-neighbor (NN) and next-nearest-neighbor (NNN) hopping on the Bethe lattice is computed at half-filling and in the weakly doped regime using the self-energy functional approach for dynamical mean-field theory. NNN hopping breaks the particle-hole symmetry and leads to a strong asymmetry of the electron-doped and hole-doped regimes. Phase separation occurs at and near half-filling, and the critical temperature of the Mott transition is strongly suppressed.

• K. Byczuk, M. Kollar, K. Held, Y.-F. Yang, I. A. Nekrasov, Th. Pruschke, and D. Vollhardt,
  Kinks in the dispersion of strongly correlated electrons,
  Nature Physics 3, 168 (2007) + supplementary information [ PDF / accepted manuscript ]
  Advance online publication, 18 Feb 2007.
  Discussed in News and Views.
  Selected for condmatjournalclub.org: Journal Club for Condensed Matter Physics, 29 Oct 2007 [ PDF ].
  [cond-mat/0609594]
  

  The properties of condensed matter are determined by single-particle and collective excitations and their interactions. These quantum-mechanical excitations are characterized by an energy E and a momentum \hbar k which are related through their dispersion E_k. The coupling of two excitations may lead to abrupt changes (kinks) in the slope of the dispersion. Such kinks thus carry important information about interactions in a many-body system. For example, kinks detected at 40-70 meV below the Fermi level in the electronic dispersion of high-temperature superconductors are taken as evidence for phonon or spin-fluctuation based pairing mechanisms. Kinks in the electronic dispersion at binding energies ranging from 30 to 800 meV are also found in various other metals posing questions about their origins. Here we report a novel, purely electronic mechanism yielding kinks in the electron dispersions. It applies to strongly correlated metals whose spectral function shows well separated Hubbard subbands and central peak as, for example, in transition metal-oxides. The position of the kinks and the energy range of validity of Fermi-liquid (FL) theory is determined solely by the FL renormalization factor and the bare, uncorrelated band structure. Angle-resolved photoemission spectroscopy (ARPES) experiments at binding energies outside the FL regime can thus provide new, previously unexpected information about strongly correlated electronic systems.

• V. Pashchenko, M. Lang, B. Wolf, L. Zherlitsyna, N. Auner, O. Shchegolikhina, Yu. Pozdniakova, F. Schütz, P. Kopietz, and M. Kollar,
  Structural and magnetic investigations on new molecular quantum rings,
  Comptes Rendus Chimie 10, 89 (2007).
  

  We report on a comparative investigation of the structural and magnetic properties of three oxygen-bridged polynuclear (N = 6, 8, 10) Cu(II) cyclomethylsiloxanolate complexes, Cu₆[(MeSiO₂)₆]₂·6DMF, {Cu₈[(MeSiO₂)₈]₂·8DMF}·EtOH and {Cu₁₀[(MeSiO₂)₁₀]₂·10DMF}·6DMF. All three molecular complexes have a planar ring-shaped configuration of the copper S = 1/2 spins. The analysis of the magnetic data, with particular emphasis placed on the high-temperature behaviour, together with the structural information enables us to correlate the evolution of the exchange coupling J between the magnetic S = 1/2 centers of the quantum ring as a function of the number N of magnetic sites to the structural changes of the molecular crystals.

• X. Ren, I. Leonov, G. Keller, M. Kollar, I. Nekrasov, and D. Vollhardt,
  LDA+DMFT computation of the electronic spectrum of NiO,
  Phys. Rev. B 74, 195114 (2006) [ PDF / AIP 2006 ].
  [cond-mat/0606285]
  

  The electronic spectrum, energy gap and local magnetic moment of paramagnetic NiO are computed using the local density approximation plus dynamical mean-field theory (LDA+DMFT). To this end the noninteracting Hamiltonian obtained within the LDA is expressed in Wannier function basis, with only the five antibonding bands with mainly Ni 3d character taken into account. Complementing it by local Coulomb interactions one arrives at a material-specific many-body Hamiltonian which is solved by DMFT together with quantum Monte Carlo (QMC) simulations. The large insulating gap in NiO is found to be a result of the strong electronic correlations in the paramagnetic state. In the vicinity of the gap region, the shape of the electronic spectrum calculated in this way is in good agreement with the experimental x-ray-photoemission and bremsstrahlung-isochromat-spectroscopy results of Sawatzky and Allen. The value of the local magnetic moment computed in the paramagnetic phase (PM) agrees well with that measured in the antiferromagnetic (AFM) phase. Our results for the electronic spectrum and the local magnetic moment in the PM phase are in accordance with the experimental finding that AFM long-range order has no significant influence on the electronic structure of NiO.

• I. A. Nekrasov, K. Held, G. Keller, D. E. Kondakov, Th. Pruschke, M. Kollar, O. K. Andersen, V. I. Anisimov, and D. Vollhardt,
  Momentum-resolved spectral functions of SrVO₃ calculated by LDA+DMFT,
  Phys. Rev. B 73, 155112 (2006) [PDF / AIP 2006 ].
  [cond-mat/0508313]
  

  LDA+DMFT, the merger of density functional theory in the local density approximation and dynamical mean-field theory, has been mostly employed to calculate k-integrated spectra accessible by photoemission spectroscopy. In this paper, we calculate k-resolved spectral functions by LDA+DMFT. To this end, we employ the Nth order muffin-tin (NMTO) downfolding to set up an effective low-energy Hamiltonian with three t_2g orbitals. This downfolded Hamiltonian is solved by DMFT yielding k-dependent spectra. Our results show a renormalized quasiparticle band over a broad energy range from -0.7 eV to +0.9 eV with small "kinks" discernible in the dispersion below the Fermi energy.

• G. Keller, K. Held, V. Eyert, V. I. Anisimov, K. Byczuk, M. Kollar, I. Leonov, X. Ren, and D. Vollhardt,
  Realistic Modeling of Materials with Strongly Correlated Electrons,
  in: NIC Symposium 2006, ed. by G. Münster, D. Wolf, and M. Kremer, NIC Series, Vol. 32, pp. 183-190 (NIC Scientific Council, 2006) [PDF at fz-juelich.de].
  
  
• V. Pashchenko, B. Brendel, B. Wolf, M. Lang, K. Lyssenko, O. Shchegolikhina, Y. Molodtsova, L. Zherlitsyna, N. Auner, F. Schütz, M. Kollar, P. Kopietz, and N. Harrison,
  Synthesis, structure and magnetic properties of a novel linear Cu(II)-trimer complex,
  Eur. J. Inorg. Chem. 2005, 4617 (2005).
  

  A new hexanuclear copper(II) sandwich complex based on two 10-membered macrocyclic phenylsiloxanolate ligands, {Cu₆[(C₆H₅SiO₂)₅]₂(OH)₂(C₁₀0H₈N₂)₂}·4(DMF)·3(H₂O), was synthesized and characterized by single-crystal X-ray diffraction and measurements of the magnetic susceptibility and isothermal magnetization. The cluster compound crystallizes in the triclinic system, space group P (No. 2), with a = 14.925(3) Å, b = 16.745(2) Å, c = 23.053(3) Å, α = 83.079(9)°, β  =  84.836(13)°, γ = 65.019(17)°, and Z = 2. The unit cell contains two identical molecules, each consisting of six interacting Cu²⁺ (S = 1/2) ions. Within the molecule, the six Cu²⁺ ions are arranged in two almost linear, parallel trimers. While pairs of oxygen atoms link the Cu²⁺ ions within the trimers, single oxygen atoms residing at the ends of the trimers provide the strongest intertrimer bonds. Magnetic measurements reveal an antiferromagnetic intratrimer exchange interaction, J/kB = 85 K, as the dominant magnetic coupling of the complex. By introducing a weak antiferromagnetic intertrimer coupling, J/kB = 3.5 K, a satisfactory description of the magnetic behavior over a wide range of temperature and magnetic field is obtained. The departure of the model curves from the data at the lowest available temperature indicates the presence of additional, weak intra- and/or intermolecular interactions.

• M. Kollar, M. Eckstein, K. Byczuk, N. Blümer, P. van Dongen, M. H. Radke de Cuba, W. Metzner, D. Tanaskovic, V. Dobrosavljevic, G. Kotliar, and D. Vollhardt,
  Green functions for nearest- and next-nearest-neighbor hopping on the Bethe lattice,
  Ann. Phys. (Leipzig) 14, 642 (2005).
  [cond-mat/0504637]
  

  We calculate the local Green function for a quantum-mechanical particle with hopping between nearest and next-nearest neighbors on the Bethe lattice, where the on-site energies may alternate on sublattices. For infinite connectivity the renormalized perturbation expansion is carried out by counting all non-self-intersecting paths, leading to an implicit equation for the local Green function. By integrating out branches of the Bethe lattice the same equation is obtained from a path integral approach for the partition function. This also provides the local Green function for finite connectivity. Finally, a recently developed topological approach is extended to derive an operator identity which maps the problem onto the case of only nearest-neighbor hopping. We find in particular that hopping between next-nearest neighbors leads to an asymmetric spectrum with additional van-Hove singularities.

• M. Eckstein, M. Kollar, K. Byczuk, and D. Vollhardt,
  Hopping on the Bethe lattice: Exact results for densities of states and dynamical mean-field theory,
  Phys. Rev. B 71, 235119 (2005) [ PDF / AIP 2005 ].
  [cond-mat/0409730]
  

  We derive an operator identity which relates tight-binding Hamiltonians with arbitrary hopping on the Bethe lattice to the Hamiltonian with nearest-neighbor hopping. This provides an exact expression for the density of states (DOS) of a non-interacting quantum-mechanical particle for any hopping. We present analytic results for the DOS corresponding to hopping between nearest and next-nearest neighbors, and also for exponentially decreasing hopping amplitudes. Conversely it is possible to construct a hopping Hamiltonian on the Bethe lattice for any given DOS. These methods are based only on the so-called distance regularity of the infinite Bethe lattice, and not on the absence of loops. Results are also obtained for the triangular Husimi cactus, a recursive lattice with loops. Furthermore we derive the exact self-consistency equations arising in the context of dynamical mean-field theory, which serve as a starting point for studies of Hubbard-type models with frustration.

• F. Schütz, P. Kopietz, and M. Kollar,
  What are spin currents in Heisenberg magnets?
  Eur. J. Phys. B 41, 557 (2004).
  [cond-mat/0405312]
  

  We discuss the proper definition of the spin current operator in Heisenberg magnets subject to inhomogeneous magnetic fields. We argue that only the component of the naive "current operator" J_ij S_i x S_j in the plane spanned by the local order parameters <S_i> and <S_j> is related to real transport of magnetization. Within a mean field approximation or in the classical ground state the spin current therefore vanishes. Thus, finite spin currents are a direct manifestation of quantum correlations in the system.

• V. Pashchenko, B. Brendel, B. Wolf, M. Lang, M. Kollar, F. Schütz, P. Kopietz, Y. Molodtsova, O. Shchegolikhina, N. Auner, and J. Bats,
  Structural and magnetic investigations on a new molecular quantum magnet,
  J. Mag. Magn. Mat. 272-276, e755 (2004).
  

  We report structural and magnetic investigations on a new hexacopper (II) siloxanolate cluster compound [C₉₂H₁₀₂Cu₆N₈O₂₉Si₁₀]. The system, crystallizing in the triclinic space group P^_1 (No. 2), has two identical macromolecules per unit cell. Each cluster contains six interacting Cu²⁺ ions. We find a crossover from a 12-spin paramagnetic state at high temperatures to a 4-spin low-temperature configuration accompanied by the formation of an S=1 cluster ground state. A minimal magnetic model is discussed which may account for these observations.

• F. Schütz, M. Kollar, and P. Kopietz,
  Persistent spin currents in mesoscopic Haldane gap spin rings,
  Phys. Rev. B 69, 035313 (2004) [ PDF / AIP 2004 ].
  [cond-mat/0308230]
  

  Using a modified spin-wave approach, we show that in the presence of an inhomogeneous magnetic field or an in plane inhomogeneous electric field a mesoscopic antiferromagnetic Heisenberg ring with integer spin (i.e., a Haldane gap system) exhibits a persistent circulating spin current. Due to quantum fluctuations the current has a finite limit on the order of -g mu_B c/L at zero temperature, provided the staggered correlation length xi exceeds the circumference L of the ring, in close analogy to ballistic charge currents in mesoscopic normal metal rings. Here c is the spin-wave velocity, g is the gyromagnetic ratio and mu_B is the Bohr magneton. For xi<<L the current is exponentially suppressed.

• F. Schütz, M. Kollar, and P. Kopietz,
  Persistent spin currents in mesoscopic Heisenberg rings,
  Phys. Rev. Lett. 91, 017205 (2003) [ PDF / AIP 2003 ].
  Selected for vjnano.org: Virtual Journal of Nanoscale Science & Technology, 8/2 (2003).
  [cond-mat/0301351]
  

  We show that at low temperatures T an inhomogeneous radial magnetic field with magnitude B gives rise to a persistent magnetization current around a mesoscopic ferromagnetic Heisenberg ring. Under optimal conditions this spin current can be as large as g mu_B (T / hbar) exp ( - 2 pi (g mu_B B / Delta )^1/2 ), as obtained from leading-order spin-wave theory. Here g is the gyromagnetic factor, mu_B is the Bohr magneton, and Delta is the energy gap between the ground state and the first spin-wave excitation. The magnetization current endows the ring with an electric dipole moment.

• M. Kollar, I. Spremo, and P. Kopietz,
  Spin wave theory at constant order parameter,
  Phys. Rev. B 67, 104427 (2003) [ PDF / AIP 2003 ].
  [cond-mat/0210578]
  

  We derive the low-temperature properties of spin-S quantum Heisenberg magnets from the Gibbs free energy G(M) for fixed order parameter M. Assuming that the low-lying elementary excitations of the system are renormalized spin waves, we show that a straightforward 1/S expansion of G(M) yields qualitatively correct results for the low-temperature thermodynamics, even in the absence of long-range magnetic order. We explicitly calculate the two-loop correction to the susceptibility of the ferromagnetic Heisenberg chain and show that it quantitatively modifies the mean-field result.

• L. Bartosch, M. Kollar, and P. Kopietz,
  Ferromagnetic Luttinger liquids,
  Phys. Rev. B 67, 092403 (2003) [ PDF / AIP 2003 ].
  [cond-mat/0207383]
  

  We study weak itinerant ferromagnetism in one-dimensional Fermi systems using perturbation theory and bosonization. We find that longitudinal spin fluctuations propagate ballistically with velocity v_m << v_F, where v_F is the Fermi velocity. This leads to a large anomalous dimension in the spin-channel and strong algebraic singularities in the single-particle spectral function and in the transverse structure factor for momentum transfers q ~ 2 Delta/v_F, where 2 Delta is the exchange splitting.

• M. Kollar,
  Construction of a dispersion relation from an arbitrary density of states,
  Int. J. Mod. Phys. B 16, 3491 (2002).
  [cond-mat/0105068]
  

  The dispersion relations of energy bands in solids are characterized by their density of states, but a given density of states may originate from various band structures. We show how a spherically symmetric dispersion can be constructed for any one-band density of states. This method is applied to one-, two- and three-dimensional systems. It also serves to establish that any one-band spectrum with finite bandwidth can be obtained from a properly scaled dispersion relation in the limit of infinite dimensions.

• M. Kollar and D. Vollhardt,
  Exact analytic results for the Gutzwiller wave function with finite magnetization,
  Phys. Rev. B 65, 155121 (2002) [ PDF / AIP 2002 ].
  [cond-mat/0111043]
  

  We present analytic results for ground-state properties of Hubbard-type models in terms of the Gutzwiller variational wave function with non-zero values of the magnetization m. In dimension D=1 approximation-free evaluations are made possible by appropriate canonical transformations and an analysis of Umklapp processes. We calculate the double occupation and the momentum distribution, as well as its discontinuity at the Fermi surface, for arbitrary values of the interaction parameter g, density n, and magnetization m. These quantities determine the expectation value of the one-dimensional Hubbard Hamiltonian for any symmetric, monotonically increasing dispersion epsilon_k. In particular for nearest-neighbor hopping and densities away from half filling the Gutzwiller wave function is found to predict ferromagnetic behavior for sufficiently large interaction U.

• M. Kollar and S. Sachdev,
  Tunneling gap of two laterally separated quantum Hall systems,
  Phys. Rev. B 65, R121304 (2002) [ PDF / AIP 2002 ].
  [cond-mat/0106001]
  

  We use a method of matched asymptotics to determine the energy gap of two counter-propagating, strongly interacting, quantum Hall edge states. The microscopic edge state dispersion and Coulomb interactions are used to precisely constrain the short-distance behavior of an integrable field theory, which then determines the low energy spectrum. We discuss the relationship of our results to the tunneling measurements of Kang et al., Nature 403, 59 (2000).

• D. Vollhardt, N. Blümer, K. Held, and M. Kollar,
  Metallic ferromagnetism - an electronic correlation phenomenon,
  in: Band-Ferromagnetism: Ground-State and Finite-Temperature Phenomena,
  edited by K. Baberschke, M. Donath, and W. Nolting,
  Lecture Notes in Physics, Vol. 580 (Springer, Heidelberg, 2001), pp. 191-207.
  [cond-mat/0012203]
  

  New insights into the microscopic origin of itinerant ferromagnetism were recently gained from investigations of electronic lattice models within dynamical mean-field theory (DMFT). In particular, it is now established that even in the one-band Hubbard model metallic ferromagnetism is stable at intermediate values of the interaction U and density n on regular, frustrated lattices. Furthermore, band degeneracy along with Hund's rule couplings is very effective in stabilizing metallic ferromagnetism in a broad range of electron fillings. DMFT also permits one to investigate more complicated correlation models, e.g., the ferromagnetic Kondo lattice model with Coulomb interaction, describing electrons in manganites with perovskite structure. Here we review recent results obtained with DMFT which help to clarify the origin of band-ferromagnetism as a correlation phenomenon.

• M. Kollar and D. Vollhardt,
  Correlated hopping of electrons: Effect on the Brinkman-Rice transition and the stability of metallic ferromagnetism,
  Phys. Rev. B 63, 045107 (2001) [ PDF / AIP 2001 ].
  [cond-mat/0008015]
  

  We study the Hubbard model with bond-charge interaction (correlated hopping) in terms of the Gutzwiller wave function. We show how to express the Gutzwiller expectation value of the bond-charge interaction in terms of the correlated momentum-space occupation. This relation is valid in all spatial dimensions. We find that in infinite dimensions, where the Gutzwiller approximation becomes exact, the bond-charge interaction lowers the critical Hubbard interaction for the Brinkman-Rice metal-insulator transition. The bond-charge interaction also favors ferromagnetic transitions, especially if the density of states is not symmetric and has a large spectral weight below the Fermi energy.

• M. Kollar and D. Vollhardt,
  Thermodynamically consistent equilibrium properties of normal-liquid Helium-3,
  Phys. Rev. B 61, 15347 (2000) [ PDF / AIP 2000 ];
  Erratum: ibid. 72, 139903 (2005) [ PDF / AIP 2005 ].
  Helium3Kalkulator (Java applet).
  [cond-mat/9906222]
  

  The high-precision data for the specific heat C_V(T,V) of normal-liquid Helium-3 obtained by Greywall, taken together with the molar volume V(T₀,P) at one temperature T₀, are shown to contain the complete thermodynamic information about this phase in zero magnetic field. This enables us to calculate the T and P dependence of all equilibrium properties of normal-liquid Helium-3 in a thermodynamically consistent way for a wide range of parameters. The results for the entropy S(T,P), specific heat at constant pressure C_P(T,P), molar volume V(T,P), compressibility kappa(T,P), and thermal expansion coefficient alpha(T,P) are collected in the form of figures and tables. This provides the first complete set of thermodynamically consistent values of the equilibrium quantities of normal-liquid Helium-3. We find, for example, that alpha(T,P) has a surprisingly intricate pressure dependence at low temperatures, and that the curves alpha(T,P) vs T do not cross at one single temperature for all pressures, in contrast to the curves presented in the comprehensive survey of helium by Wilks.
  Corrected in cond-mat/9906222v3: The sign of the coefficient d₀ was misprinted in Table I of cond-mat/9906222v1 and v2. It now correctly reads d₀=-7.1613436. All results in the paper were obtained with the correct value of d_0. (We would like to thank for E. Collin, H. Godfrin, and Y. Bunkov for finding this misprint.)

• N. Chandra, M. Kollar, and D. Vollhardt,
  Nearly universal crossing point of the specific heat curves of Hubbard models,
  Phys. Rev. B 59, 10541 (1999) [ PDF / AIP 1999 ].
  [cond-mat/9810391]
  

  A nearly universal feature of the specific heat curves C(T,U) vs. T for different U of a general class of Hubbard models is observed. That is, the value C₊ of the specific heat curves at their high-temperature crossing point T₊ is almost independent of lattice structure and spatial dimension d, with C₊/k_B approx 0.34. This surprising feature is explained within second order perturbation theory in U by identifying two small parameters controlling the value of C₊: the integral over the deviation of the density of states N(E) from a constant value, characterized by dN = int |N(E)-1/2| dE, and the inverse dimension, 1/d.

• D. Vollhardt, N. Blümer, K. Held, M. Kollar, J. Schlipf, M. Ulmke, and J. Wahle,
  Metallic ferromagnetism: Progress in our understanding of an old strong-coupling problem,
  Advances in Solid State Physics 38, 383 (1999).
  [cond-mat/9804112]
  

  Metallic ferromagnetism is in general an intermediate to strong coupling phenomenon. Since there do not exist systematic analytic methods to investigate such types of problems, the microscopic origin of metallic ferromagnetism is still not sufficiently understood. However, during the last two or three years remarkable progress was made in this field: It is now certain that even in the one-band Hubbard model metallic ferromagnetism is stable in dimensions d=1, 2, and infinity on regular lattices and at intermediate values of the interaction U and density n. In this paper the basic questions and recent insights regarding the microscopic conditions favoring metallic ferromagnetism in this model are reviewed. These findings are contrasted with the results for the orbitally degenerate case.

• M. Kollar,
  Magnetische und thermodynamische Eigenschaften korrelierter Fermionensysteme,
  ISBN-3-89639-150-X (Wißner-Verlag, Augsburg, 1998), Dissertation.
  
  
• D. Vollhardt, N. Blümer, K. Held, M. Kollar, J. Schlipf, and M. Ulmke,
  Non-perturbative approaches to magnetism in strongly correlated electron systems,
  Z. Phys. B 103, 283 (1997).
  [cond-mat/9701150]
  

  The microscopic basis for the stability of itinerant ferromagnetism in correlated electron systems is examined. To this end several routes to ferromagnetism are explored, using both rigorous methods valid in arbitrary spatial dimensions, as well as Quantum Monte Carlo investigations in the limit of infinite dimensions (dynamical mean-field theory). In particular we discuss the qualitative and quantitative importance of (i) the direct Heisenberg exchange coupling, (ii) band degeneracy plus Hund's rule coupling, and (iii) a high spectral density near the band edges caused by an appropriate lattice structure and/or kinetic energy of the electrons. We furnish evidence of the stability of itinerant ferromagnetism in the pure Hubbard model for appropriate lattices at electronic densities not too close to half-filling and large enough U. Already a weak direct exchange interaction, as well as band degeneracy, is found to reduce the critical value of U above which ferromagnetism becomes stable considerably. Using similar numerical techniques the Hubbard model with an easy axis is studied to explain metamagnetism in strongly anisotropic antiferromagnets from a unifying microscopic point of view.

• M. Kollar, R. Strack, and D. Vollhardt,
  Ferromagnetism in correlated electron systems: Generalization of Nagaoka's theorem,
  Phys. Rev. B 53, 9225 (1996) [ PDF / AIP 1996 ];
  erratum: ibid. 55, E11878 (1997) [ PDF / AIP 1997 ].
  [cond-mat/9511060]
  

  Nagaoka's theorem on ferromagnetism in the Hubbard model with one electron less than half filling is generalized to the case where all possible nearest-neighbor Coulomb interactions (the density-density interaction V, bond-charge interaction X, exchange interaction F, and hopping of double occupancies F') are included. It is shown that for ferromagnetic exchange coupling (F>0) ground states with maximum spin are stable already at finite Hubbard interaction U>U_c. For non-bipartite lattices this requires a hopping amplitude t<=0. For vanishing F one obtains U_c=infinity as in Nagaoka's theorem. This shows that the exchange interaction F is important for stabilizing ferromagnetism at finite U. Only in the special case X=t the ferromagnetic state is stable even for F=0, provided the lattice allows the hole to move around loops.





I don't want to achieve immortality through my work;
I want to achieve immortality through not dying.
- Woody Allen