## **Quantum Monte Carlo Simulations**

## Prof. Dr. Alejandro Muramatsu

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).

*Last change: 1999-01-19, Volker Eyert*