Tight-binding billiards

• URL: http://arxiv.org/abs/2206.07078v2
• Date: Wed, 14 Sep 2022 07:29:55 GMT
• Title: Tight-binding billiards
• Authors: Iris Ul\v{c}akar and Lev Vidmar
• Abstract summary: We show that many properties of tight-binding billiards match those of quantum-chaotic quadratic Hamiltonians. On the other hand, a degenerate subset of single-particle eigenstates at zero energy can be described as chiral particles whose wavefunctions are confined to one of the sublattices.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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