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Measurement phase transitions in the no-click limit as quantum phase transitions of a non-hermitean vacuum
by Caterina Zerba, Alessandro Silva
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Submission summary
| Authors (as registered SciPost users): | Alessandro Silva · Caterina Zerba |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2301.07383v1 (pdf) |
| Date submitted: | 2023-01-19 09:17 |
| Submitted by: | Zerba, Caterina |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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.
Current status:
Reports on this Submission
Anonymous Report 1 on 2023-3-27 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2301.07383v1, delivered 2023-03-27, doi: 10.21468/SciPost.Report.6904
Strengths
1. Suggests an easy and accessible way to study measurement-induced phase transitions, and proposes and extension of the area-law theorem to non-Hermitian Hamiltonians.
2. Extensively discusses the validity of the assumptions underlying the work and provides numerical evidences to support the discussion.
3. Provides sufficiently detailed analytics in order to reproduce the analysis and the results.
4. Gives proper background and references to motivate this work
Weaknesses
1. The manuscript suffers from some imprecisions on the numerical results
2. The figures are not sufficiently described and commented in the main text
Report
In their manuscript Zerba and Silva provide a novel way to study measurement-induced phase transitions by the means of the no-click limit. In this regime, the dynamics of a system boils down to a non-unitary dynamics piloted by a non-Hermitian Hamiltonian. The authors show that the properties of the system are essentially captured by the non-Hermitian vaccum of the Hamiltonian. They also claim that the scaling of the bi-partite entanglement entropy with the subsystem size undergoes a phase transition that is correlated to the gapped or not nature of the spectrum of the Hamiltonian.
In order to support their claim, the authors provide numerical evidences based on the study of two one-dimensional integrable models : the transverse-field Ising model and the long-range Kitaev chain. They also test the consistency of their approach by introducing sparse clicks from the measurement device to which the many-body system is coupled to.
Despite the high interest of this work in the domain of measurement-induced phase transitions, the manuscript lacks clarity and an effort is required in order to properly highlight the novelty of these results.
Requested changes
1. Most of the analytical results provided in Sec 2. could be moved in the Appendix for the sake of clarity.
2. Figure 3 does enable the reader to 4assess whether the difference between $S_{zc}$ and $S_v$ is sizeable or not. I would instead suggest to plot the relative error $(S_{zc}-S_v)/S_{vc}$.
3. How many trajectories where used to evaluate the average showed on Fig 5(c) ? It would also be useful to show on the same plot the $c$ as a function of $\gamma$ in the no-click case for comparison of the critical behaviour of the transition (position of the critical point, finite-size effects)