Tight-binding billiards

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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Cited by in corpus (13)

• Pauli Spectrum and Non-stabilizerness of Typical Quantum Many-Body States
• Generalized Deep Thermalization for Free Fermions
• Localization challenges quantum chaos in the finite two-dimensional Anderson model
• Generalized thermalization in quantum-chaotic quadratic Hamiltonians
• Phenomenology of quantum eigenstates in mixed-type systems: lemon billiards with complex phase space structure
• Eigenstate entanglement entropy in the integrable spin-$\frac{1}{2}$ XYZ model
• Single-quasiparticle eigenstate thermalization
• Symmetry classification of typical quantum entanglement
• Critical quantum dynamics of observables at eigenstate transitions
• Average Rényi Entanglement Entropy in Gaussian Boson Sampling
• Haldane graphene billiards versus relativistic neutrino billiards
• Localization transitions in quadratic systems without quantum chaos
• Solvable random matrix ensemble with a logarithmic weakly confining potential