Universal Aspects of High-Temperature Relaxation Dynamics in Random Spin Models
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arXiv
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| Format: | Preprint |
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2023
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| _version_ | 1866909570300903424 |
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| author | Zhou, Tian-Gang Zheng, Wei Zhang, Pengfei |
| author_facet | Zhou, Tian-Gang Zheng, Wei Zhang, Pengfei |
| contents | 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 $A=-ξ_1^2+ξ_2^2-4ξ_2ξ_3+ξ_3^2$. Here $(ξ_1,ξ_3,ξ_3)$ characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for $A>0$, with frequency $Ω\propto \sqrt{A}$. 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2305_02359 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Universal Aspects of High-Temperature Relaxation Dynamics in Random Spin Models Zhou, Tian-Gang Zheng, Wei Zhang, Pengfei Strongly Correlated Electrons Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics High Energy Physics - Theory 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 $A=-ξ_1^2+ξ_2^2-4ξ_2ξ_3+ξ_3^2$. Here $(ξ_1,ξ_3,ξ_3)$ characterizes the anisotropy of the Heisenberg interaction. Furthermore, the oscillation shows up only for $A>0$, with frequency $Ω\propto \sqrt{A}$. 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. |
| title | Universal Aspects of High-Temperature Relaxation Dynamics in Random Spin Models |
| topic | Strongly Correlated Electrons Disordered Systems and Neural Networks Quantum Gases Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2305.02359 |