Eigenstate thermalization hypothesis and integrability in quantum spin chains

By V. Alba. 2014

132 citations recorded by the source corpus.

We investigate the eigenstate thermalization hypothesis (ETH) in integrable models, focusing on the spin-1/2 isotropic Heisenberg (XXX) chain. We provide numerical evidence that ETH holds for typical eigenstates (weak ETH scenario). Specifically, using a numerical implementation of state-of-the-art Bethe ansatz results, we study the finite-size scaling of the eigenstate-to-eigenstate fluctuations of the reduced density matrix. We find that fluctuations are normally distributed, and their standard deviation decays in the thermodynamic limit as L^{-1/2}, with L the size of the chain. This is in contrast with the exponential decay that is found in generic non-integrable systems. Based on our results, it is natural to expect that this scenario holds in other integrable spin models and for typical local observables. Finally, we investigate the entanglement properties of the excited states of the XXX chain. We numerically verify that typical mid-spectrum eigenstates exhibit extensive entanglement entropy (i.e., volume-law scaling).

Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics

View Paper: https://www.semanticscholar.org/paper/a74b0a1dc7091f1e0427cd5f9903e62fb76d4fcb

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In Atomic and Molecular Physics, and Optics

1. L. Vidmar
2. Tomaz Prosen
3. J. Bonvca
4. Jan vSuntajs
5. Marcos Rigol
6. V. Khemani
7. Juan P. Garrahan
8. J. Dubail

In Condensed Matter Physics

1. J. Bonvca
2. Jan vSuntajs
3. Marcos Rigol
4. Tomaz Prosen
5. L. Vidmar

Citations in the corpus

• Generalized Gibbs ensemble in integrable lattice models (2016, background): “In this case one finds that they exhibit a narrow distribution centered about the mean value predicted by traditional statistical mechanics, with a standard deviation that vanishes with increasing system size (as 1/ √ L [118]).”
• Ergodicity breaking transition in finite disordered spin chains (2020, background): “A well-established nonergodic behavior in translationally invariant systems occurs at integrable points [8– 16], for which eigenstates do not obey ETH [17–25] and the long-time averages of observables after quantum quenches are described by the generalized Gibbs ensemble [23, 26].”