Generalized thermalization in quantum-chaotic quadratic Hamiltonians

Abstract

Thermalization (generalized thermalization) in nonintegrable (integrable) quantum systems requires two ingredients: equilibration and agreement with the predictions of the Gibbs (generalized Gibbs) ensemble. We prove that observables that exhibit eigenstate thermalization in single-particle sector equilibrate in many-body sectors of quantum-chaotic quadratic models. Remarkably, the same observables do not exhibit eigenstate thermalization in many-body sectors (we establish that there are exponentially many outliers). Hence, the generalized Gibbs ensemble is generally needed to describe their expectation values after equilibration, and it is characterized by Lagrange multipliers that are smooth functions of single-particle energies.

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• Macroscopic Irreversibility in Quantum Systems: Free Expansion in a Fermion Chain
• Critical quantum dynamics of observables at eigenstate transitions
• Quadratic Hamiltonian approach to heat transport in fermionic systems
• Thermalization is typical in large classical and quantum harmonic systems
• Timescales and necessary conditions for hydrodynamization in one-dimensional Bose gases
• On the difference between thermalization in open and isolated quantum systems: a case study
• Equilibration of Non-interacting Photons and Quantum Signatures of Chaos
• Mean Field Decoupling of Single Impurity Anderson Model through Auxiliary Majorana Fermions