Entanglement and purification transitions in non-Hermitian quantum mechanics

TL;DR

This paper investigates a spectral phase transition in non-Hermitian quantum systems under continuous measurement, revealing a transition from mixed states with volume-law entanglement to pure, low-entanglement states as post-selection rate increases.

Contribution

It identifies a spectral phase transition linked to an exceptional point and PT symmetry breaking in non-Hermitian Hamiltonians, with detailed analysis using exact diagonalization and mean-field theory.

Findings

Spectral phase transition occurs at a critical post-selection rate.

Below the transition, states remain mixed and develop volume-law entanglement.

Above the transition, states approach a pure, low-entanglement steady state.

Abstract

A quantum system subject to continuous measurement and post-selection evolves according to a non-Hermitian Hamiltonian. We show that, as one increases the rate of post-selection, this non-Hermitian Hamiltonian undergoes a spectral phase transition. On one side of this phase transition (for weak post-selection) an initially mixed density matrix remains mixed at all times, and an initially unentangled state develops volume-law entanglement; on the other side, an arbitrary initial state approaches a unique pure state with low entanglement. We identify this transition with an exceptional point in the spectrum of the non-Hermitian Hamiltonian, at which PT symmetry is spontaneously broken. We characterize the transition as well as the nontrivial steady state that emerges at late times in the mixed phase using exact diagonalization and an approximate, analytically tractable mean-field theory; these methods yield consistent conclusions.