Monte Carlo calculation for systems consisting of several coordinate patches

TL;DR

This paper examines how Monte Carlo simulations for systems with multiple coordinate patches depend on the time step, proposing an improved kinetic term to align Monte Carlo results with Hamiltonian calculations in gauge theory.

Contribution

The paper introduces an improved kinetic term that ensures Monte Carlo simulations converge to the same spectrum as Hamiltonian methods for multi-patch coordinate systems.

Findings

Naive kinetic term fails to match Hamiltonian spectra.

Improved kinetic term achieves convergence with Rayleigh-Ritz results.

Enhanced method applies to intermediate volume SU(2) gauge theory.

Abstract

I investigate the time step dependence of Monte Carlo simulations for coordinate-spaces consisting of several patches. It is shown that a naive kinetic term does not necessarily converge to the same spectrum as a Hamiltonian calculation. Then an improved kinetic term is presented which allows one to connect the Monte Carlo and Rayleigh-Ritz results of intermediate volume SU(2) gauge theory.