Universal Critical Behaviors in Non-Hermitian Phase Transitions

TL;DR

This paper uncovers universal critical behaviors in non-Hermitian quantum phase transitions using density functional theory, revealing scaling laws for observables and entanglement at transition points, and establishing foundational insights for quantum metrology.

Contribution

It introduces a novel application of density functional theory to non-Hermitian systems, revealing universal behaviors and scaling laws in phase transitions that were previously unknown.

Findings

Universal scaling laws for physical observables at non-Hermitian phase transitions.

Universal scaling behaviors of quantum entanglement at critical points.

Connection between nonanalytic behavior of steady states and phase transitions.

Abstract

Quantum phase transitions also occur in non-Hermitian systems. In this work we show that density functional theory, for the first time, uncovers universal behaviors for phase transitions in non-Hermitian many-body systems. To be specific, we first prove that the non-degenerate steady state of a non-Hermitian quantum many-body system is a universal function of the first derivative of the steady state energy with respect to the control parameter. This finding has far-reaching consequences for non-Hermitian systems: (i) It bridges the nonanalytic behavior in physical observable and nonanalytic behavior of steady state energy, which explains why the quantum phase transitions in non-Hermitian systems occur for finite systems. (ii) It predicts universal scaling behaviors of any physical observable at non-Hermitian phase transition point with scaling exponent being $(1-1/p),2(1-1/p),\cdots,n(1-1/p),\cdots$ with $p$ being the number of coalesced states at the exceptional point and $n$ being a positive integer. (iii). It reveals that quantum entanglement in non-Hermitian phase transition point presents universal scaling behaviors with critical exponents being $(1-1/p),2(1-1/p),\cdots,n(1-1/p),\cdots$. These results uncover universal critical behaviors in non-Hermitian phase transitions and provide profound connections between entanglement and phase transition in non-Hermitian quantum many-body physics and establish foundations for quantum metrology in non-Hermitian systems.