碎片化的ETH：预热、时间尺度和系综不等价
Fragmented ETH and Ensemble Inequivalence
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中文总结 AI 辅助
研究具有强长程相互作用的有限量子系统趋近热平衡的情况，揭示其两阶段平衡过程及非普遍性，发展微扰理论，提出碎片化本征态热化假设，解释系综不等价，结果适用于一类哈密顿量。
中文摘要 AI 辅助
我们研究具有强长程相互作用的有限量子系统如何趋近热平衡。从全连接极限继承的近守恒量使希尔伯特空间碎片化，导致多体谱分裂成能带。结果，平衡异常缓慢，通过长寿命的预热平台进行。然而，这种两阶段平衡过程并不普遍。我们揭示了决定哪些可观测量和初始态表现出或规避预热平台的机制。我们还发展了一种微扰理论，给出了预热平台高度及其时间尺度的解析表达式。尽管缺乏全局遍历性，但量子混沌在各个能带内发展，支持了能带分辨的热化表述，即碎片化本征态热化假设（fETH）。与传统ETH不同，fETH中的有限尺寸标度遵循对称强加的选择规则，限制了可比较的系统尺寸。这种能带分辨描述对平衡统计力学有直接影响。微正则系综局限于单个能带，而正则系综混合不同能带。这种不匹配解释了系综不等价，而无需调用平衡相变。我们的结果适用于一类广泛的表现出希尔伯特空间碎片化的哈密顿量。
英文摘要
We investigate thermalization in finite quantum systems with strong long-range interactions. Nearly conserved quantities inherited from the fully connected limit organize the Hilbert space into weakly coupled sectors and split the many-body spectrum into energy bands. Despite the resulting breakdown of global ergodicity, quantum chaos develops within individual energy bands, enabling the definition of microcanonical ensembles within the bands. This supports a band-resolved formulation of thermalization, which we term fragmented eigenstate thermalization hypothesis (fETH). Unlike conventional ETH, finite-size scaling in fETH obeys a symmetry-imposed selection rule that restricts which system sizes can be compared. This band-resolved description has consequences for equilibrium statistical mechanics. While microcanonical ensembles remain confined to a single band, canonical ensembles mix different bands. This mismatch explains ensemble inequivalence without invoking equilibrium phase transitions. Our results apply broadly to Hamiltonians near a fully permutation-symmetric limit.
发表机构
- University of Connecticut（康涅狄格大学）
- Tata Institute of Fundamental Research（塔塔基础研究所）
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