Thermalization and its mechanism for generic isolated quantum systems

By Marcos Rigol, V. Dunjko, M. Olshanii. Nature, 2007

2,694 citations recorded by the source corpus.

An understanding of the temporal evolution of isolated many-body quantum systems has long been elusive. Recently, meaningful experimental studies of the problem have become possible, stimulating theoretical interest. In generic isolated systems, non-equilibrium dynamics is expected to result in thermalization: a relaxation to states in which the values of macroscopic quantities are stationary, universal with respect to widely differing initial conditions, and predictable using statistical mechanics. However, it is not obvious what feature of many-body quantum mechanics makes quantum thermalization possible in a sense analogous to that in which dynamical chaos makes classical thermalization possible. For example, dynamical chaos itself cannot occur in an isolated quantum system, in which the time evolution is linear and the spectrum is discrete. Some recent studies even suggest that statistical mechanics may give incorrect predictions for the outcomes of relaxation in such systems. Here we demonstrate that a generic isolated quantum many-body system does relax to a state well described by the standard statistical-mechanical prescription. Moreover, we show that time evolution itself plays a merely auxiliary role in relaxation, and that thermalization instead happens at the level of individual eigenstates, as first proposed by Deutsch and Srednicki. A striking consequence of this eigenstate-thermalization scenario, confirmed for our system, is that knowledge of a single many-body eigenstate is sufficient to compute thermal averages—any eigenstate in the microcanonical energy window will do, because they all give the same result.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7aab2cff793bca6c3a4051cf049c2eec472d5479

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In Atomic and Molecular Physics, and Optics

1. V. Khemani
2. A. Nahum
3. Pasquale Calabrese
4. D. Abanin
5. D. Huse
6. Matthew Fisher
7. L. Vidmar
8. I. Bloch

In Statistical and Nonlinear Physics

1. Pasquale Calabrese
2. V. Khemani
3. B. Doyon
4. L. Vidmar
5. Juan P. Garrahan
6. Tomaz Prosen
7. J. Caux
8. A. Nahum

Citations in the corpus

• Entanglement scaling of operators: a conformal field theory approach, with a glimpse of simulability of long-time dynamics in 1  +  1d (2016, background): “In the past years, there has been a lot of work on the problem of equilibration in closed quantum systems, and on generalized Gibbs ensembles (GGE), motivated by [41, 42].”
• Observation of many-body localization of interacting fermions in a quasirandom optical lattice (2015, background): “Hence, ergodicity is responsible for the demise of observable quantum correlations in the dynamics of large many-body systems and forms the basis for the emergence of local thermodynamic equilibrium in isolated quantum systems [2, 3, 4].”
• Local integrals of motion in many‐body localized systems (2016, methodology): “The structure of the MBL eigenstates is inherently incompatible with the Eigenstate Thermalization Hypothesis (ETH) formulated in [36, 56, 88, 97] as a microscopic justification for quantum thermalization.”
• Entanglement in a fermion chain under continuous monitoring (2018, background): “The dynamics of entanglement in many-body systems is a topic under intensive study, as entanglement is a fundamental notion of quantum physics, deeply tied to basic issues such as thermalization of closed quantum systems [1–4], holography [5–7], quantum chaos and information scrambling [8, 9].”
• Aspects of non-equilibrium in classical and quantum systems: Slow relaxation and glasses, dynamical large deviations, quantum non-ergodicity, and open quantum dynamics (2017, background): “oir.For references see e.g., [60, 61, 62, 63, 64, 65]. Quantum thermalisation can be seen as a consequence of the spectrum of a many-body system obeying the eigenstate thermalisation hypothesis (ETH) [66, 67, 68, 69]. When ETH holds, the spectrum of such a system is similar - in the large size limit”
• Velocity-dependent Lyapunov exponents in many-body quantum, semiclassical, and classical chaos (2018, background): “[3] Marcos Rigol, Vanja Dunjko, and Maxim Olshanii, “Thermalization and its mechanism for generic isolated quantum systems,” Nature 452, 854–858 (2008).”
• Generalized Gibbs ensemble in integrable lattice models (2016, background): “This has been shown to occur in numerical studies of nonintegrable systems [74, 86, 87, 88].”
• Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “[11] Marcos Rigol, Vanja Dunjko, and Maxim Olshanii, “Thermalization and its mechanism for generic isolated quantum systems,” Nature 452, 854–8 (2008).”