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- DFG Research Group: Project 7

**Quantum Monte Carlo Simulations**

In systems with strong electronic correlations, like the vanadium oxides considered here, numerical simulations frequently offer the only possibility to obtain reliable results, even in the realm of crude and symplifying models. The aim of this project was to investigate the metal-insulator transition of V_{2}O_{3} and other transition metal chalcogenides using quantum Monte Carlo simulations of the three-dimensional Hubbard model. In a first step the spin correlation function of lattices up to 1000 sites has been calculated. Extrapolating the data to an infinite large system the Néel-temperature, i.e. the critical temperature for the transition to an antiferromagnetic phase, could be determined as a function of the interaction strength U. Substantial discrepancies compared to the results of older QMC simulations were observed confirming the necessity of a careful analysis of finite-size effects. On the other hand, comparison with the phase boundary calculated in Dynamical Mean Field theory (DMFT) yielded good agreement for low and intermediate values of U.

The transition from the metallic to the insulating paramagnetic phase, which occurs with increasing interaction strength above the Néel-temperature, was also investigated. In principle, the frequency-dependent conductivity can be extracted from Monte Carlo data of dynamical correlation functions using the maximum-entropy method. However, the computational effort to obtain results of reasonable numerical accuracy turned out to be extremely large for the three-dimensional lattices considered here. Therefore we restricted the simulations to the analysis of static correlation functions and thermodynamic quantities. From the behavior of the specific heat, the kinetic energy and the local magnetic moment as a function of U the crossover region from the metallic to the insulating phase could be determined. Again, the results were in good agreement with DMFT data.

The simulations were performed on a 4-nodes parallel computer by Parsytec, which had been acquired for this project, on the 14-nodes IBM SP computer of the University of Augsburg, and on the computers of the Leibniz-Rechenzentrum in Munich. The Munich computers are a 72-nodes IBM SP2 computer, a vector computer Cray T90/4 and a vector-parallel computer SNI/Fujitsu VPP 700 with 52 nodes. To run the program on the parallel machines it was optimized using the communication software *Message-Passing Interface* (MPI).

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- 18.03.2016