Entropic analysis of quantum phase transitions from uniform to spatially inhomogeneous phases

TL;DR

This paper introduces an entropic method to analyze quantum phase transitions in low-dimensional systems, detecting inhomogeneous phases through von Neumann entropy and Fourier spectrum analysis.

Contribution

It presents a novel entropic approach based on the length dependence of von Neumann entropy to identify spatially inhomogeneous quantum phases.

Findings

Peaks at nonzero wave vectors indicate oscillatory correlations.

The method effectively distinguishes uniform from inhomogeneous phases.

Applicable to fermionic and spin models in low dimensions.

Abstract

We propose a new approach to study quantum phase transitions in low-dimensional fermionic or spin models that go from uniform to spatially inhomogeneous phases such as dimerized, trimerized, or incommensurate phases. It is based on studying the length dependence of the von Neumann entropy and its corresponding Fourier spectrum for finite segments in the ground state of finite chains. Peaks at a nonzero wave vector are indicators of oscillatory behavior in decaying correlation functions.