Title: Unstable periodic orbits galore and quantum hyperscarring in highly frustrated magnets Show Chinese title

Title: 大量不稳定的周期轨道和高度受挫磁体中的量子超聚焦

Abstract: Highly frustrated magnets, with their macroscopically-degenerate classical ground states and massively-entangled quantum spin liquid phases, have been pivotal to the development of modern condensed matter concepts such as emergent symmetries, topological order, and fractionalisation. The effects of frustration and massive degeneracies at high energy, where the many-body dynamics becomes chaotic, have hitherto been far less explored. Here, we identify a high-energy dynamical analog of highly-frustrated magnetism, in the form of an extensive manifold of classical ''interaction-suppressing'' configurations giving rise to unstable periodic orbits. These are in general neither protected by symmetry nor integrability, and emerge from a set of dynamical local constraints that effectively nullify the interactions while allowing extensively many local degrees of freedom. The proliferation of unstable periodic orbits corresponds in the quantum case to ''hyperscarring'', that is, quantum scarring on exponentially many unstable periodic orbits. On the product states associated to the latter, the amplitudes of the mid-spectrum thermal eigenstates exhibit a power-law distribution, in stark contrast to the expected exponential Porter-Thomas distribution that holds for generic product states. Our results reveal a new constrained dynamical regime where many-body quantum chaos coexists with structured manifolds of coherent dynamics, and establishes a mechanism for hitherto elusive extensive scarring. Show Chinese abstract

Abstract: 高度受挫的磁体，因其宏观简并的经典基态和大量纠缠的量子自旋液体相，对于现代凝聚态概念的发展至关重要，如涌现对称性、拓扑序和分数化。 在高能区域，由于多体动力学变得混沌，受挫和大量简并效应至今研究较少。 在这里，我们识别出一种高能动态类比的高度受挫磁性，表现为一个广泛的经典“相互作用抑制”配置流形，导致不稳定的周期轨道。 这些周期轨道通常既不被对称性保护，也不可积，它们来源于一组动力学局部约束，这些约束有效地消除了相互作用，同时允许广泛数量的局部自由度。 在量子情况下，不稳定周期轨道的大量存在对应于“超疤痕”，即在指数级多的不稳定周期轨道上的量子疤痕。 在后者的产物态上，中谱热态的振幅表现出幂律分布，这与通用产物态所预期的指数波特-托马斯分布形成鲜明对比。 我们的结果揭示了一个新的受限动力学区域，在该区域内，多体量子混沌与结构化的相干动力学流形共存，并建立了一个此前难以捉摸的广泛疤痕机制。