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Excitations and ergodicity of critical quantum spin chains from non-equilibrium classical dynamics
by Stéphane Vinet, Gabriel Longpré, William Witczak-Krempa
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Submission summary
| Authors (as registered SciPost users): | Gabriel Longpre · Stéphane Vinet · William Witczak-Krempa |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2107.04615v2 (pdf) |
| Date submitted: | 2021-08-10 17:54 |
| Submitted by: | Longpre, Gabriel |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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Abstract
We study a quantum spin-1/2 chain that is dual to the canonical problem of non-equilibrium Kawasaki dynamics of a classical Ising chain coupled to a thermal bath. The Hamiltonian is obtained for the general disordered case with non-uniform Ising couplings. The quantum spin chain (dubbed Ising-Kawasaki) is stoquastic, and depends on the Ising couplings normalized by the bath's temperature. We give its exact ground states. Proceeding with uniform couplings, we study the one- and two-magnon excitations. Solutions for the latter are derived via a Bethe Ansatz scheme. In the antiferromagnetic regime, the two-magnon branch states show intricate behavior, especially regarding their hybridization with the continuum. We find that that the gapless chain hosts multiple dynamics at low energy as seen through the presence of multiple dynamical critical exponents. Finally, we analyze the full energy level spacing distribution as a function of the Ising coupling. We conclude that the system is non-integrable for generic parameters, or equivalently, that the corresponding non-equilibrium classical dynamics are ergodic.
Current status:
Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2022-1-30 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2107.04615v2, delivered 2022-01-30, doi: 10.21468/SciPost.Report.4282
Strengths
- The model and analysis are mostly presented clearly.
- The model appears to display some interesting phenomena such as glassiness and anomalous dynamics.
Weaknesses
- Ultimately it is not clear what the significance of the results is.
- The section on dynamical exponents is confusing. I am not sure what the result/claim is. The authors have access to the two-particle spectrum for all parameters so they should be able to settle the issue of how the excitation gap scales with size. Is the claim that the two-particle spectrum always has z = 2 but there could be other excitations that are slower? Could the value of kappa play any role here?
Report
I think this work does an interesting and apparently valid calculation.
Requested changes
Rewrite the section on dynamical critical exponents to make the claims more precise.