Title: Universal Dephasing Mechanism of Many-Body Quantum Chaos Show Chinese title

Title: 多体量子混沌的普遍退相机制

Abstract: Ergodicity is a fundamental principle of statistical mechanics underlying the behavior of generic quantum many-body systems. However, how this universal many-body quantum chaotic regime emerges due to interactions remains largely a puzzle. This paper demonstrates using both heuristic arguments and a microscopic calculation that a dephasing mechanism, similar to Altshuler-Aronov-Khmelnitskii dephasing in the theory of localization, underlies this transition to chaos. We focus on the behavior of the spectral form factor (SFF) as a function of "time", t, which characterizes level correlations in the many-body spectrum. The SFF can be expressed as a sum over periodic classical orbits and its behavior hinges on the interference of trajectories related to each other by a time translation. In the absence of interactions, time-translation symmetry is present for each individual particle, which leads to a fast exponential growth of the SFF and correspondingly loss of correlations between many-body levels. Interactions lead to dephasing, which disrupts interference, and breaks the massive time-translation symmetry down to a global time-translation/energy conservation. This in turn gives rise to the hallmark linear-in-$t$ ramp in the SFF reflecting Wigner-Dyson level repulsion. This general picture is supported by a microscopic analysis of an interacting many-body model. Specifically, we study the complex $\mbox{SYK}_2+\mbox{SYK}_2^2$ model, which allows to tune between an integrable and chaotic regime. It is shown that the dephasing mass vanishes in the former case, which maps to the non-interacting $\mbox{SYK}_2$ model via a time reparameterization. In contrast, the chaotic regime gives rise to dephasing, which suppresses the exponential ramp of the non-interacting theory and induces correlations between many-body levels. Show Chinese abstract

Abstract: 遍历性是统计力学的基本原理，它支撑着通用量子多体系统的行为。 然而，由于相互作用，这种普遍的多体量子混沌区域是如何出现的，仍然 largely 是一个谜。 本文通过启发式论证和微观计算证明，一种去相位机制，类似于局域化理论中的 Altshuler-Aronov-Khmelnitskii 去相位，支撑着这一向混沌的转变。 我们关注谱形因子（SFF）作为“时间”t 的函数的行为，该函数表征多体谱中的能级相关性。 SFF 可以表示为周期经典轨道的总和，其行为取决于由时间平移相关的轨迹之间的干涉决定。 在没有相互作用的情况下，每个单独粒子都存在时间平移对称性，这会导致 SFF 快速指数增长，并相应地导致多体能级之间的相关性丧失。 相互作用导致去相位，这会破坏干涉，并将大规模的时间平移对称性分解为全局的时间平移/能量守恒。 这进而导致 SFF 中标志性的与$t$成线性关系的斜坡，反映了 Wigner-Dyson 能级排斥。 这一总体图景得到了对一个相互作用多体模型的微观分析的支持。 具体来说，我们研究了复杂的$\mbox{SYK}_2+\mbox{SYK}_2^2$模型，该模型允许在可积和混沌区域之间调节。 结果表明，在前一种情况下，去相位质量消失，这通过时间重参数化映射到非相互作用的$\mbox{SYK}_2$模型。 相反，混沌区域产生去相位，抑制非相互作用理论的指数斜坡，并在多体能级之间引入相关性。