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Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations
by Oleksandr Gamayun, Oleg Lychkovskiy
This is not the latest submitted version.
Submission summary
| Authors (as registered SciPost users): | Oleksandr Gamayun · Oleg Lychkovskiy |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2110.13123v2 (pdf) |
| Date submitted: | Oct. 27, 2021, 10:37 a.m. |
| Submitted by: | Oleg Lychkovskiy |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
The Kitaev model on the honeycomb lattice, while being integrable via the spin-fermion mapping, has generally resisted an analytical treatment of the far-from-equilibrium dynamics due to the extensive number of relevant configurations of conserved charges. Here we study a close proxy of this model, the isotropic Kitaev spin-$1/2$ model on the Bethe lattice. Instead of relying on the spin-fermion mapping, we take a straightforward approach of solving Heisenberg equations for a tailored subset of spin operators. The simplest operator in this subset corresponds to the energy contribution of a single bond direction. As an example, we calculate the time-dependent expectation value of this observable for a factorized translation-invariant (or staggered-translation-invariant) initial state with arbitrary initial (staggered) polarization.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2021-12-19 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2110.13123v2, delivered 2021-12-19, doi: 10.21468/SciPost.Report.4064
Strengths
- innovative idea to access time evolution of kitaev model and in general of a number of interesting many-body system
Weaknesses
- clarifications and some extra checks needed
Report
The idea of using Heisenberg time evolution in many-body systems is usually overlooked, and this paper is a great example of how instead it can be a very useful tool. I recommend publication provided the following points are carefully addressed:
- include a broader introduction of the model, write the Hamiltonian in Pauli matrices and clarify why the Bethe lattice is easier to access with this method compared to hexagonal and other lattices.
- compare the final result with exact results available for quenches with initial states where single fermionic sector can be used
- clarify the meaning of operator of eq 16 and write an explicit derivation of eq 14-19, possible in appendices.
- the large time limit of eq 35 can be reduced to a single integral, reminding of diagonal ensemble. Is there a GGE associated to the large time value of correlator?
Requested changes
see report.
Report #1 by Benjamin Doyon (Referee 1) on 2021-12-17 (Invited Report)
- Cite as: Benjamin Doyon, Report on arXiv:2110.13123v2, delivered 2021-12-17, doi: 10.21468/SciPost.Report.4062
Strengths
Interesting technical idea, showing that it works (proof of concept)
Potential for many new results of interest in quantum many-body
Weaknesses
Report
I do not have any specific comment for improvement, I believe this is publishable as is.