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

Zerba, Caterina; Silva, Alessandro

doi:10.21468/SciPostPhysCore.6.3.051

SciPost Physics Core

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

Caterina Zerba, Alessandro Silva

SciPost Phys. Core 6, 051 (2023) · published 18 July 2023

doi: 10.21468/SciPostPhysCore.6.3.051
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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 Schrödinger 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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhysCore.6.3.051
TI  - Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum
PY  - 2023/07/18
UR  - https://scipost.org/SciPostPhysCore.6.3.051
JF  - SciPost Physics Core
JA  - SciPost Phys. Core
VL  - 6
IS  - 3
SP  - 051
A1  - Zerba, Caterina
AU  - Silva, Alessandro
AB  - 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 Schrödinger 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.
ER  -

@Article{10.21468/SciPostPhysCore.6.3.051,
	title={{Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum}},
	author={Caterina Zerba and Alessandro Silva},
	journal={SciPost Phys. Core},
	volume={6},
	pages={051},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhysCore.6.3.051},
	url={https://scipost.org/10.21468/SciPostPhysCore.6.3.051},
}

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¹ ² ³ ⁴ Caterina Zerba,
² Alessandro Silva