Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum

TL;DR

This paper investigates dynamical phase transitions in non-Hermitian quantum systems, revealing entanglement behaviors analogous to vacuum phase transitions and suggesting a generalization of the area-law theorem.

Contribution

It demonstrates that entanglement phase transitions in non-Hermitian Hamiltonian models mirror vacuum phase transitions, extending the understanding of entanglement in non-Hermitian quantum systems.

Findings

Bounded entanglement entropy with gapped imaginary spectrum

Logarithmic entanglement growth with gapless imaginary spectrum

Potential to generalize the area-law theorem to non-Hermitian Hamiltonians

Abstract

We study dynamical phase transitions occurring in the stationary state of the dynamics of integrable many-body non-hermitian Hamiltonians, which can be either realized as a no-click limit of a stochastic Schr\"{o}dinger equation or using spacetime duality of quantum circuits. In two specific models, the Transverse Field Ising Chain and the Long Range Kitaev Chain, we observe that the entanglement phase transitions occurring in the stationary state have the same nature as that occurring in the vacuum of the non-hermitian Hamiltonian: bounded entanglement entropy when the imaginary part of the quasi-particle spectrum is gapped and a logarithmic growth for gapless imaginary spectrum. This observation suggests the possibility to generalize the area-law theorem to non-Hermitian Hamiltonians.