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Quantum chaos and ensemble inequivalence of quantum long-range Ising chains
Physical Review B ( IF 3.2 ) Pub Date : 2021-09-27 , DOI: 10.1103/physrevb.104.094309
Angelo Russomanno 1 , Michele Fava 2 , Markus Heyl 1
Affiliation  

We use large-scale exact diagonalization to study the quantum Ising chain in a transverse field with long-range power-law interactions decaying with exponent α. We numerically study various probes for quantum chaos and eigenstate thermalization on the level of eigenvalues and eigenstates. The level-spacing statistics yields a clear sign towards a Wigner-Dyson distribution and therefore towards quantum chaos across all values of α>0. Yet, for α<1 we find that the microcanonical entropy is nonconvex. This is due to the fact that the spectrum is organized in energetically separated multiplets for α<1. While quantum chaotic behavior develops within the individual multiplets, many multiplets do not overlap and do not mix with each other, as we analytically and numerically argue. Our findings suggest that a small fraction of the multiplets could persist at low energies for α1 even for large N, giving rise to ensemble inequivalence.

中文翻译:

量子长程伊辛链的量子混沌和系综不等价

我们使用大规模精确对角化来研究横向场中的量子伊辛链,其中长程幂律相互作用随指数衰减 α. 我们在本征值和本征态水平上数值研究了量子混沌和本征态热化的各种探针。水平间距统计数据对 Wigner-Dyson 分布产生了明显的迹象,因此对所有值的量子混沌α>0. 然而,对于α<1我们发现微正则熵是非凸的。这是因为光谱被组织成能量分离的多重峰α<1. 虽然量子混沌行为在单个多重态内发展,但正如我们在分析和数值上争论的那样,许多多重态不重叠也不相互混合。我们的研究结果表明,一小部分多重态可以在低能量下持续存在α1 即使对于大 N,导致集合不等价。
更新日期:2021-09-28
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