Algorithms for the Markov Entropy Decomposition

TL;DR

The paper introduces numerical algorithms for the Markov entropy decomposition (MED), a cluster-based method for simulating finite temperature quantum systems, demonstrating its accuracy and flexibility on the 2D XXZ model.

Contribution

It provides detailed algorithms for MED, including solving minimization problems and extracting physical responses, enhancing the method's applicability.

Findings

MED accurately identifies critical points in the 2D XXZ model

MED outperforms exact diagonalization in accuracy

MED offers greater flexibility for quantum system simulations

Abstract

The Markov entropy decomposition (MED) is a recently-proposed, cluster-based simulation method for finite temperature quantum systems with arbitrary geometry. In this paper, we detail numerical algorithms for performing the required steps of the MED, principally solving a minimization problem with a preconditioned Newton's algorithm, as well as how to extract global susceptibilities and thermal responses. We demonstrate the power of the method with the spin-1/2 XXZ model on the 2D square lattice, including the extraction of critical points and details of each phase. Although the method shares some qualitative similarities with exact-diagonalization, we show the MED is both more accurate and significantly more flexible.