Tight-binding billiards

TL;DR

This paper introduces two-dimensional tight-binding billiards with curved boundaries, showing they exhibit quantum-chaotic properties such as entanglement entropy and eigenstate thermalization, despite lacking disorder.

Contribution

It demonstrates that disorder-free, curved-boundary tight-binding models can replicate key features of quantum-chaotic quadratic Hamiltonians.

Findings

Entanglement entropy matches random matrix theory predictions.

Single-particle observables obey eigenstate thermalization.

Zero-energy modes are confined to sublattices.

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.