Bipartite reweight-annealing algorithm of quantum Monte Carlo to extract large-scale data of entanglement entropy and its derivative

TL;DR

This paper introduces a reweight-annealing quantum Monte Carlo method for efficiently extracting large-scale entanglement entropy data and its derivative, aiding phase transition and critical point analysis.

Contribution

The proposed scheme enables high-precision, large-scale entanglement entropy computation with a novel reweight-annealing approach and a simple formula for EE derivatives, improving efficiency and applicability.

Findings

Successfully computes large-scale EE data across parameters

Demonstrates accurate detection of phase transitions and critical exponents

Simplifies EE derivative calculation without numerical differentiation

Abstract

We propose a quantum Monte Carlo scheme capable of extracting large-scale data of R\'enyi entanglement entropy (EE) with high precision and low technical barrier. Instead of directly computing the ratio of two partition functions within different space-time manifolds, we obtain them separately via a reweight-annealing scheme and connect them from the ratio of a reference point. The incremental process can thus be designed along a path of real physical parameters within this framework, and all intermediates are meaningful EEs corresponding to these parameters. In a single simulation, we can obtain many multiples ($\sim \beta L^d$, d is the space dimension) of EEs, which has been proven to be powerful for determining phase transition points and critical exponents. Additionally, we introduce a formula to calculate the derivative of EE without resorting to numerical differentiation from dense EE data. This formula only requires computing the difference of energies in different space-time manifolds. The calculation of EE and its derivative becomes much cheaper and simpler in our scheme. We then demonstrate the feasibility of using EE and its derivative to find phase transition points, critical exponents, and various phases.