SciPost Submission Page
Universal Aspects of High-Temperature Relaxation Dynamics in Random Spin Models
by Tian-Gang Zhou, Wei Zheng, Pengfei Zhang
Submission summary
| Authors (as registered SciPost users): | Pengfei Zhang |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2305.02359v2 (pdf) |
| Date submitted: | 2024-06-30 23:42 |
| Submitted by: | Zhang, Pengfei |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
Universality is a crucial concept in modern physics, allowing us to capture the essential features of a system's behavior using a small set of parameters. In this work, we unveil universal spin relaxation dynamics in anisotropic random Heisenberg models with infinite-range interactions at high temperatures. Starting from a polarized state, the total magnetization can relax monotonically or decay with long-lived oscillations, determined by the sign of a universal single function $A=-\xi_1^2+\xi_2^2-4\xi_2\xi_3+\xi_3^2$. Here $(\xi_1,\xi_3,\xi_3)$ characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for $A>0$, with frequency $\Omega \propto \sqrt{A}$. To validate our theory, we compare it to numerical simulations by solving the Kadanoff-Baym (KB) equation with a melon diagram approximation and the exact diagonalization (ED). The results show our theoretical prediction works in both cases, regardless of a small system size $N=8$ in ED simulations. Our study sheds light on the universal aspect of quantum many-body dynamics beyond low energy limit.
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
Report
The authors calculate the relaxation dynamics of the magnetization for an infinite range anisotropic Heisenberg model staring from a high temperature initial condition. These are computed from Kadanoff Baym equations on the Schwinger Keldysh contour. These equations are linearized and numerically solved and compared to exact diagonalization. Hence it is established that the magnetization exhibits either monotonic decay or long lived oscillations, depending on a single anisotropy parameter
The results seem valid, and the investigation seems thorough. At the same time the scope seems relatively narrow. I think this can be published more or less as is, but I would think this is more suited to SciPost Physics Core.
Recommendation
Accept in alternative Journal (see Report)
Report #1 by Subir Sachdev (Referee 2) on 2024-9-18 (Invited Report)
Report
This is a well written paper containing important new results on the non-equilibrium dynamics of a strongly interacting quantum system at high temperature. The analytic analysis generalizes the Sachdev-Ye melon diagram equations to include spin anisotropy and Keldysh contours. These results are nicely compared to numerics.
I gladly recommend publication after the following change:
The discussion in the abstract and the introduction gives the reader the impression that the authors have developed a theory which is independent of the melon-diagram Kadanoff-Byam equations. Thus e.g. the abstract states:
"To validate our theory, we compare it to numerical simulations by solving the Kadanoff-Baym (KB) equation with a melon diagram approximation...."
In fact, the theory is also obtained from the KB equations with a melon diagram approximation, and this is not the impression one gets from such a sentence. It seems to me that only the ED study is beyond such an approximation.
There is a similar issue with the introduction.
I think this can be easily cleared up with changes in the language.
Recommendation
Ask for minor revision