Identifying the maximum entropy method as a special limit of stochastic analytic continuation

TL;DR

This paper demonstrates that the maximum entropy method is a special limit of stochastic analytic continuation, using a classical field system analogy and Monte Carlo sampling, with improvements via parallel tempering.

Contribution

It reveals the maximum entropy method as a mean field limit of stochastic analytic continuation and introduces a parallel tempering algorithm for better phase space exploration.

Findings

Maximum entropy is a mean field limit of stochastic analytic continuation.

A classical field mapping enables a new perspective on analytic continuation.

Parallel tempering improves sampling efficiency and phase space traversal.

Abstract

The maximum entropy method is shown to be a special limit of the stochastic analytic continuation method introduced by Sandvik [Phys. Rev. B 57, 10287 (1998)]. We employ a mapping between the analytic continuation problem and a system of interacting classical fields. The Hamiltonian of this system is chosen such that the determination of its ground state field configuration corresponds to an unregularized inversion of the analytic continuation input data. The regularization is effected by performing a thermal average over the field configurations at a small fictitious temperature using Monte Carlo sampling. We prove that the maximum entropy method, the currently accepted state of the art, is simply the mean field limit of this fully dynamical procedure. We also describe a technical innovation: we suggest that a parallel tempering algorithm leads to better traversal of the phase space and makes it easy to identify the critical value of the regularization temperature.