Tight-binding billiards

Iris Ulčakar; Lev Vidmar

doi:10.1103/physreve.106.034118

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arXiv · 2206.07078

Tight-binding billiards

Iris Ulčakar·Lev Vidmar

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Abstract

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 non-interacting 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 wavefunctions are confined to one of the sublattices.

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cond-mat.stat-mech cond-mat.dis-nn cond-mat.mes-hall quant-ph

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Iris Ulčakar, Lev Vidmar. 2022-06-14. Tight-binding billiards. https://doi.org/10.1103/physreve.106.034118

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