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Entanglement transitions in SU(1, 1) quantum dynamics: applications to Bose-Einstein condensates and periodically driven coupled oscillators
by Heng-Hsi Li, Po-Yao Chang
Submission summary
| Authors (as registered SciPost users): | Po-Yao Chang |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2405.12558v1 (pdf) |
| Date submitted: | 2024-05-23 09:46 |
| Submitted by: | Chang, Po-Yao |
| Submitted to: | SciPost Physics Core |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We study the entanglement properties in non-equilibrium quantum systems with the SU(1, 1) structure. Through M\"obius transformation, we map the dynamics of these systems following a sudden quench or a periodic drive onto three distinct trajectories on the Poincar\'e disc, corresponding the heating, non-heating, and a phase boundary describing these non-equilibrium quantum states. We consider two experimentally feasible systems where their quantum dynamics exhibit the SU(1, 1) structure: the quench dynamics of the Bose-Einstein condensates and the periodically driven coupled oscillators. In both cases, the heating, non-heating phases, and their boundary manifest through distinct signatures in the phonon population where exponential, oscillatory, and linear growths classify these phases. Similarly, the entanglement entropy and negativity also exhibit distinct behaviors (linearly, oscillatory, and logarithmic growths) characterizing these phases, respectively. Notibly, for the periodically driven coupled oscillators, the non-equilibrium properties are characterized by two sets of SU(1, 1) generators. The corresponding two sets of the trajectories on two Poincar\'e discs lead to a more complex phase diagram. We identify two distinct phases within the heating region discernible solely by the growth rate of the entanglement entropy, where a discontinuity is observed when varying the parameters across the phase boundary within in heating region. This discontinuity is not observed in the phonon population.
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The authors consider the entanglement measures of various systems described by SU(1,1) algebra, driven by quantum quenches or periodic protocols. I think the results are interesting and the paper deserves to be published in Scipost Physics Core after addressing my comments.
1. It it not obvious which quantity is k dependent and which is not. For example, after Eq. (37), the xi_{0,1,2}(k) are defined, by \xi is k independent and later \xi_{0,1,2} appear without the k argument. I find this confusing here and at other places. Similarly, in Fig. 1, n_k and S_k appears without specifying the k values.
2. For Sec. 4, there is a momentum sum for the BEC Hamiltonian, but later this sum is omitted. Is it due to the peculiar initial state?
3. What happens if there are also other terms in the Hamiltonian which do not preserve the SU(1,1) algebraic structures. Maybe distinct the generators of distinct k modes are coupled to each other or some non-linear powers of the generators appear?
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