Replacing energy by von Neumann entropy in quantum phase transitions

TL;DR

This paper proposes using the non-analytic behavior of von Neumann entropy as a universal indicator of quantum phase transitions, including cases where traditional energy-based criteria fail, such as Anderson localization.

Contribution

It introduces von Neumann entropy as a new criterion for detecting quantum phase transitions, especially in complex systems where energy criteria are insufficient.

Findings

Von Neumann entropy exhibits non-analyticities at quantum critical points.

The entropy shows fractal scaling at the Anderson transition.

Non-analyticities in entropy correlate with quantum phase transitions in dissipative systems.

Abstract

In the thermodynamic limit two distinct states of matter cannot be analytic continuations of each other. Classical phase transitions are characterized by non-analyticities of the free energy. For quantum phase transitions (QPTs) the ground state energy often assumes the role of the free energy. But in a number of important cases this criterion fails to predict a QPT, such as the three-dimensional metal-insulator transition of non-interacting electrons in a random potential (Anderson localization). It is therefore essential that we find alternative criteria that can track fundamental changes in the internal correlations of the ground state wavefunction. Here we propose that QPTs are generally accompanied by non-analyticities of the von Neumann (entanglement) entropy. In particular, the entropy is non-analytic at the Anderson transition, where it exhibits unusual fractal scaling. We also examine two dissipative quantum systems of considerable interest to the study of decoherence and find that non-analyticities occur if and only if the system undergoes a QPT.