格点规范理论中阶梯预热化的起源
Origin of staircase prethermalization in lattice gauge theories
摘要：
具有精确局域规范对称性的量子多体系统表现出丰富的非平衡物理，如约束动力学和无无序局域化。在一份联合来文中[J.C. Halimeh和P.Hauke，arXiv：2004.07248]，我们提出了\textit{staircase prethermalization}在$\mathrm{Z}_2$格点规范理论的规范不变性的一个小的破坏的证据。在这里，我们巩固这一发现和相关的紧急非微扰的时间尺度分析和数值。通过马格努斯展开，我们证明了不同规范不变超扇区之间的精确共振是阶梯预热化出现的主要原因。此外，我们展示了我们的结论对各种初始条件，包括不同的系统大小，物质填充，规范不变的部门，除了各种边界条件，如不同的最大现场物质占领的鲁棒性。我们还详细说明了我们的结论是如何独特的局部对称模型，为什么他们打破了全球对称性破缺的情况下。此外，我们将我们的结果扩展到$\mathrm{U}(1)$格点规范理论，说明我们的研究结果的一般性。我们的工作为格点规范理论的约束动力学提供了一个分析基础，并证明了规范理论动力学对实验设置中的误差具有一定的内在鲁棒性。
英文摘要：
Quantum many-body systems with exact local gauge symmetries exhibit rich out-of-equilibrium physics such as constrained dynamics and disorder-free localization. In a joint submission [J. C. Halimeh and P. Hauke, arXiv:2004.07248], we present evidence of \textit{staircase prethermalization} in a $\mathrm{Z}_2$ lattice gauge theory subjected to a small breaking of gauge invariance. Here, we consolidate this finding and the associated emergent nonperturbative timescales analytically and numerically. By means of a Magnus expansion, we demonstrate how exact resonances between different gauge-invariant supersectors are the main reason behind the emergence of staircase prethermalization. Furthermore, we showcase the robustness of our conclusions against various initial conditions including different system sizes, matter fillings, and gauge-invariance sectors, in addition to various boundary conditions, such as different maximal on-site matter occupations. We also elaborate on how our conclusions are unique to local-symmetry models and why they break down in the case of global-symmetry breaking. We moreover extend our results to $\mathrm{U}(1)$ lattice gauge theories, illustrating the generality of our findings. Our work offers an analytic footing into the constrained dynamics of lattice gauge theories and provides proof of a certain intrinsic robustness of gauge-theory dynamics to errors in experimental settings.
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