Tight-binding billiards

• Published in: arXiv.org
• Main Authors: Ulčakar, Iris, Vidmar, Lev
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 14.09.2022
• Subjects: Binding; Eigenvectors; Fermions; Lattice vibration; Matrix theory; Physics - Disordered Systems and Neural Networks; Physics - Mesoscale and Nanoscale Physics; Physics - Quantum Physics; Physics - Statistical Mechanics; Thermalization (energy absorption); Wave functions
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2206.07078

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.