CP$^{N-1}$ model with the theta term and maximum entropy method

TL;DR

This paper explores using the maximum entropy method to compute the partition function in lattice field theories with a theta term, effectively addressing the flattening problem caused by errors in topological charge distribution data.

Contribution

It introduces applying the maximum entropy method as an alternative to Fourier transform for calculating the partition function in the CP$^{N-1}$ model, especially in cases affected by flattening.

Findings

MEM agrees with Fourier transform in non-flattening cases

MEM produces smooth results in flattening cases

MEM effectively mitigates the sign problem in lattice simulations

Abstract

A $\theta$ term in lattice field theory causes the sign problem in Monte Carlo simulations. This problem can be circumvented by Fourier-transforming the topological charge distribution $P(Q)$. This strategy, however, has a limitation, because errors of $P(Q)$ prevent one from calculating the partition function ${\cal Z}(\theta)$ properly for large volumes. This is called flattening. As an alternative approach to the Fourier method, we utilize the maximum entropy method (MEM) to calculate ${\cal Z}(\theta)$. We apply the MEM to Monte Carlo data of the CP$^3$ model. It is found that in the non-flattening case, the result of the MEM agrees with that of the Fourier transform, while in the flattening case, the MEM gives smooth ${\cal Z}(\theta)$.