Tight-binding billiards

Area of Science:

• Quantum physics
• Condensed matter theory
• Statistical mechanics

Background:

• Previous studies confirmed universal entanglement and thermalization in quantum-chaotic quadratic Hamiltonians.
• These Hamiltonians typically incorporate random terms, acting as a source of disorder.

Purpose of the Study:

• To investigate quantum-chaotic properties in a disorder-free system.
• To explore tight-binding billiards as a model for quantum chaos.
• To examine entanglement entropy and eigenstate thermalization in this novel system.

Main Methods:

• Introduction of two-dimensional tight-binding billiards with noninteracting spinless fermions.
• Utilizing a disorder-free square lattice with curved hard-wall boundaries.
• Analysis of many-body eigenstates and single-particle observables.

Main Results:

• Tight-binding billiards exhibit properties consistent with quantum-chaotic quadratic Hamiltonians.
• Average entanglement entropy aligns with random matrix theory predictions.
• One-body observables in single-particle eigenstates satisfy the single-particle eigenstate thermalization hypothesis.
• A subset of zero-energy modes (zero modes) displays chiral particle behavior, with wave functions localized to sublattices.

Conclusions:

• Tight-binding billiards serve as a valuable disorder-free model for studying quantum chaos.
• Universal quantum chaotic properties can emerge even in the absence of disorder.
• The observed chiral behavior of zero modes offers new insights into topological properties in quantum systems.