SciPost Submission Page
Quench dynamics of entanglement from crosscap states
by Konstantinos Chalas, Pasquale Calabrese, Colin Rylands
Submission summary
| Authors (as registered SciPost users): | Konstantinos Chalas |
| Submission information | |
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| Preprint Link: | scipost_202412_00036v1 (pdf) |
| Date submitted: | Dec. 18, 2024, 3:36 p.m. |
| Submitted by: | Chalas, Konstantinos |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The linear growth of entanglement after a quench from a state with short-range correlations is a universal feature of many body dynamics. It has been shown to occur in integrable and chaotic systems undergoing either Hamiltonian, Floquet or circuit dynamics and has also been observed in experiments. The entanglement dynamics emerging from long-range correlated states is far less studied, although no less viable using modern quantum simulation experiments. In this work, we investigate the dynamics of the bipartite entanglement entropy and mutual information from initial states which have long-range entanglement with correlation between antipodal points of a finite and periodic system. Starting from these crosscap states, we study both brickwork quantum circuits and Hamiltonian dynamics and find distinct patterns of behaviour depending on the type of dynamics and whether the system is integrable or chaotic. Specifically, we study both dual unitary and random unitary quantum circuits as well as free and interacting fermion Hamiltonians. For integrable systems, we find that after a time delay the entanglement experiences a linear in time decrease followed by a series of revivals, while, in contrast, chaotic systems exhibit constant entanglement entropy. On the other hand, both types of systems experience an immediate linear decrease of the mutual information in time. In chaotic systems this then vanishes, whereas integrable systems instead experience a series of revivals. We show how the quasiparticle and membrane pictures of entanglement dynamics can be modified to describe this behaviour, and derive explicitly the quasiparticle picture in the case of free fermion models which we then extend to all integrable systems.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Current status:
Reports on this Submission
Strengths
1- Investigates a new type of quench 2- Examines multiple cases (quantum circuits and spin chains, both ergodic and integrable) 3- Includes both analytical and numerical analyses 4- Provides physical interpretations 5- Well-written
Weaknesses
Report
Based on the specific models studied, the authors observe that in chaotic systems, entanglement entropy remains constant, whereas in integrable systems, it initially stays constant but eventually begins to decrease. For chaotic systems, mutual information decreases until it vanishes and remains zero, while in integrable systems, it decreases initially but later increases again.
Requested changes
The article contains several points that could benefit from clarification:
1) The discussion of Random Unitary Circuits could be elaborated further, particularly regarding the origin of equation (2.34).
2) What is meant by "a specific class of dual unitary gates" prior to equation (2.44)? Does this refer to all chaotic gates? Additionally, what does "for large enough z" signify in equation (2.44)?
3) In equation (3.8), why is N_A conserved? The commutation [N,H]=0 alone is insufficient; some condition on the initial state must also be specified.
4) There appears to be a parenthesis mismatch in equation (3.9).
5) In the case of the XXZ spin chain, the description of bound states and the TBA are valid in the infinite L limit. However, the crosscap state is ill-defined in this limit. Does this not lead to a contradiction?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)
Strengths
- it performs a systematic study of quantum quenches from initial states with a large amount of long-range entanglement.
- both brickwork quantum circuits and Hamiltonian dynamics have been studied; both integrable and chaotic systems have been studied; analytical and numerical results are compared when possible.
- it proposes modifications to the quasiparticle and membrance picture that were previously established for studying entanglement dynamics.
Weaknesses
Report
The paper by Chalas et al. studies quench dynamics in several cases starting from crosscap states. These states have special structure in that lattice sites that are separated by a long distance are entangled. In most previous studies about quantum quenches, the initial states are chosen to be simple ones with low entanglement (product states or eigenstates of certain Hamiltonians). Going beyond this paradigm can potentially reveal some other interesting phenomena. This paper makes a good step along this direction. The investigations are quite comprehsive and sufficient details are given. Physical implications have been unveiled based on suitable generalization of the quasiparticle and membrane pictures.
It would be helpful to clarify a few minor issues.
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It would be good to emphasize that Eq. (1.1) is a rather general definition. It includes not only the crosscap states defined in conformal field theory (CFT), but also many other possibilities that most likely do not correspond to crosscap states in CFT.
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It should be mentioned that states like Eq. (1.1) have also been termed "entangled antipodal pair" states in some papers [Phys. Rev. Lett. 133, 170404 (2024); Phys. Rev. Res. 6, L042062 (2024); 2412.18610]
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It seems that all calculations are performed using periodic boundary conditions. Is there any special reason? When studying crosscap states in CFT, this is necessary because they are not defined for open boundary conditions. For the current setting, especially considering the possibility of experimental investigations using quantum simulators, open boundary conditions may be useful to explore.
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In the case of Hamiltonian dynamics, if one turns to models that cannot be solved exactly by Bethe ansatz, will the quasiparticle and/or membrane pictures survive? The authors may comment on this issue briefly.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Strengths
1- studies an interesting problem in various ways and settings 2- provides analytical results for unusual quenches, both chaotic and integrable 3- is nicely written
Weaknesses
1- Methods are standard 2- Some relevant calculations are left for further work
Report
The paper provides results in three quite different settings for the same nontrivial initial states and yields insights into differences in integrable and chaotic behaviour. It also discusses how the membrane picture needs to be modified for correlated initial states.
Requested changes
I would like to see the following changes, but I don't insist that all need to be addressed in this paper: - The discussion about how the membrane picture needs to be modified for correlated initial states is a bit vague and imprecise. Extending it, generalizing, and providing more details would help the paper, in my opinion. - I believe the paper would be quite a bit stronger if the recursion equation 2.35 were solved for finite q. I don't see a reason why authors would need to delegate this to further work (if it is doable). Very similar recurrences have been solved in quite a few recent works, so I expect the authors can modify the procedure, for example, https://arxiv.org/pdf/2004.13697. If this does not work, authors can at least comment about why it is more difficult. - Authors can provide a short explanation of why and when Eq. 2.44 holds (apart from citing 54). This approximation gives zero correlations, so in some sense loses all microscopic. -Label under Figure 7. There is probably a typo of->or. They mention random unitaries, but do they mean their q->infinity limit?
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)