Entanglement and purification transitions in non-Hermitian quantum mechanics

Published

April 30, 2021

Author(s)

Michael Gullans, Sarang Gopalakrishnan

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 can undergo 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, analyti- cally tractable mean-field theory; these methods yield consistent conclusions.

Citation

Physical Review Letters

Volume

126

Issue

17

Pub Type

Journals

Download Paper

https://doi.org/10.1103/PhysRevLett.126.170503

Local Download

Citation

Gullans, M. and Gopalakrishnan, S. (2021), Entanglement and purification transitions in non-Hermitian quantum mechanics, Physical Review Letters, [online], https://doi.org/10.1103/PhysRevLett.126.170503, https://tsapps.nist.gov/publication/get_pdf.cfm?pub_id=931658 (Accessed October 15, 2025)