Tight-binding billiards,Physical Review E

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Tight-binding billiards
Physical Review E ( IF 2.2 ) Pub Date : 2022-09-12 , DOI: 10.1103/physreve.106.034118
Iris Ulčakar ₁ , Lev Vidmar ₁

Affiliation

Recent works have established universal entanglement properties and demonstrated validity of single-particle eigenstate thermalization in quantum-chaotic quadratic Hamiltonians. However, a common property of all quantum-chaotic quadratic Hamiltonians studied in this context so far is the presence of random terms that act as a source of disorder. Here we introduce tight-binding billiards in two dimensions, which are described by noninteracting spinless fermions on a disorder-free square lattice subject to curved open (hard-wall) boundaries. We show that many properties of tight-binding billiards match those of quantum-chaotic quadratic Hamiltonians: The average entanglement entropy of many-body eigenstates approaches the random matrix theory predictions and one-body observables in single-particle eigenstates obey the single-particle eigenstate thermalization hypothesis. On the other hand, a degenerate subset of single-particle eigenstates at zero energy (i.e., the zero modes) can be described as chiral particles whose wave functions are confined to one of the sublattices.

中文翻译：

紧身台球

最近的工作已经建立了普遍的纠缠特性，并证明了量子混沌二次哈密顿量中单粒子本征态热化的有效性。然而，到目前为止，在这种情况下研究的所有量子混沌二次哈密顿量的一个共同特性是存在作为无序来源的随机项。在这里，我们介绍了二维的紧束缚台球，这些台球由无序方形晶格上的非相互作用无自旋费米子描述，该晶格受弯曲的开放（硬壁）边界影响。我们表明，紧束缚台球的许多特性与量子混沌二次哈密顿量相匹配：多体本征态的平均纠缠熵接近随机矩阵理论的预测，单粒子本征态中的单体可观测量服从单粒子本征态热化假设。另一方面，零能量（即零模式）的单粒子本征态的退化子集可以描述为手性粒子，其波函数被限制在一个子晶格中。

更新日期：2022-09-13

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