The role of winding numbers in quantum Monte Carlo simulations

Abstract

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.

5 pages, 5 figures

References in corpus (2)

• Cluster Algorithm for Vertex Models
• Superfluid Bosons and Flux Liquids: Disorder, Thermal Fluctuations, and Finite-Size Effects

Cited by in corpus (5)

• The Power of Adiabatic Quantum Computation with No Sign Problem
• Nontrivial worldline winding in non-Hermitian quantum systems
• Stoquasticity in circuit QED
• Classical fully-packed loop model with attractive interactions on the square lattice
• 1D Spontaneous Symmetry Breaking in thermal equilibrium via Non-Hermitian Construction