Application of Maximum Entropy Method to Lattice Field Theory with a Topological Term

TL;DR

This paper explores using the maximum entropy method to improve the analysis of topological charge distributions in lattice field theory, addressing the flattening problem caused by errors in Fourier-transform-based methods at larger volumes.

Contribution

The paper introduces the application of the maximum entropy method to lattice field theory with a theta term, offering a solution to the flattening issue in topological charge distribution analysis.

Findings

MEM significantly reduces flattening effects

Improves accuracy of topological charge distribution analysis

Enables study of phase structure at larger volumes

Abstract

In Monte Carlo simulation, lattice field theory with a $\theta$ term suffers from the sign problem. This problem can be circumvented by Fourier-transforming the topological charge distribution $P(Q)$. Although this strategy works well for small lattice volume, effect of errors of $P(Q)$ becomes serious with increasing volume and prevents one from studying the phase structure. This is called flattening. As an alternative approach, we apply the maximum entropy method (MEM) to the Gaussian $P(Q)$. It is found that the flattening could be much improved by use of the MEM.