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Tight-binding billiards.

Iris Ulčakar1, Lev Vidmar1

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This study introduces disorder-free tight-binding billiards, revealing universal quantum chaos properties like entanglement entropy and eigenstate thermalization without random disorder. Zero energy modes exhibit chiral behavior confined to sublattices.

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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.