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 1 by Subir Sachdev 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