Generalized Deep Thermalization for Free Fermions
arXiv:2207.13628 · doi:10.1103/PhysRevA.107.032215
Abstract
In non-interacting isolated quantum systems out of equilibrium, local subsystems typically relax to non-thermal stationary states. In the standard framework, information on the rest of the system is discarded, and such states are described by a Generalized Gibbs Ensemble (GGE), maximizing the entropy while respecting the constraints imposed by the local conservation laws. Here we show that the latter also completely characterize a recently introduced projected ensemble (PE), constructed by performing projective measurements on the rest of the system and recording the outcomes. By focusing on the time evolution of fermionic Gaussian states in a tight-binding chain, we put forward a random ensemble constructed out of the local conservation laws, which we call deep GGE (dGGE). For infinite-temperature initial states, we show that the dGGE coincides with a universal Haar random ensemble on the manifold of Gaussian states. For both infinite and finite temperatures, we use a Monte Carlo approach to test numerically the predictions of the dGGE against the PE. We study in particular the -moments of the state covariance matrix and the entanglement entropy, finding excellent agreement. Our work provides a first step towards a systematic characterization of projected ensembles beyond the case of chaotic systems and infinite temperatures.
13 pages, 4 figures; v2: minor revision
References in corpus (12)
- Thermalization and its mechanism for generic isolated quantum systems
- Quantum Quench in the Transverse Field Ising Chain
- Experimental Observation of a Generalized Gibbs Ensemble
- Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
- Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
- Quantum Quench in the Transverse Field Ising Chain II: Stationary State Properties
- From Interacting Particles to Equilibrium Statistical Ensembles
- Correlations and diagonal entropy after quantum quenches in XXZ chains
- Solvable model of deep thermalization with distinct design times
- Symmetry-resolved Page curves
- Tight-binding billiards
- High-temperature thermalization implies the emergence of quantum state designs
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