The role of winding numbers in quantum Monte Carlo simulations

Details The role of winding numbers in quantum Monte Carlo simulations The role of winding numbers in quantum Monte Carlo simulations

1997-11-12

arxiv.org/abs/cond-mat/9711110v1

Physics

Condensed Matter

Statistical Mechanics

5 pages, 5 figures

Scientific paper

10.1103/PhysRevB.57.13382

We discuss the effects of fixing the winding number in quantum Monte Carlo simulations. We present a simple geometrical argument as well as strong numerical evidence that one can obtain exact ground state results for periodic boundary conditions without changing the winding number. However, for very small systems the temperature has to be considerably lower than in simulations with fluctuating winding numbers. The relative deviation of a calculated observable from the exact ground state result typically scales as $T^{\gamma}$, where the exponent $\gamma$ is model and observable dependent and the prefactor decreases with increasing system size. Analytic results for a quantum rotor model further support our claim.

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