Precise Determination of Quantum Critical Points by the Violation of the Entropic Area Law

TL;DR

This paper introduces a new estimator based on entanglement entropy to precisely locate quantum critical points, demonstrating high accuracy and practicality compared to traditional methods in small lattice systems.

Contribution

The paper presents a novel entropic estimator for quantum critical points, outperforming the standard crossing method in accuracy and ease of implementation for small lattice sizes.

Findings

Successfully locates the quantum Ising chain critical point

Accurately finds the spin-1 Blume-Capel quantum chain critical line

Determines the tricritical point of the Blume-Capel model

Abstract

Finite-size scaling analysis turns out to be a powerful tool to calculate the phase diagram as well as the critical properties of two dimensional classical statistical mechanics models and quantum Hamiltonians in one dimension. The most used method to locate quantum critical points is the so called crossing method, where the estimates are obtained by comparing the mass gaps of two distinct lattice sizes. The success of this method is due to its simplicity and the ability to provide accurate results even considering relatively small lattice sizes. In this paper, we introduce an estimator that locates quantum critical points by exploring the known distinct behavior of the entanglement entropy in critical and non critical systems. As a benchmark test, we use this new estimator to locate the critical point of the quantum Ising chain and the critical line of the spin-1 Blume-Capel quantum chain. The tricritical point of this last model is also obtained. Comparison with the standard crossing method is also presented. The method we propose is simple to implement in practice, particularly in density matrix renormalization group calculations, and provides us, like the crossing method, amazingly accurate results for quite small lattice sizes. Our applications show that the proposed method has several advantages, as compared with the standard crossing method, and we believe it will become popular in future numerical studies.