Relaxation in a completely integrable many-body quantum system: an ab initio study of the dynamics of the highly excited states of 1D lattice hard-core bosons.

By Marcos Rigol, V. Dunjko, V. Yurovsky, M. Olshanii. Physical Review Letters, 2006

1,161 citations recorded by the source corpus.

In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such a state are. We confirm the relaxation hypothesis through an ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of physical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which have already been observed in the recent experiment on the nonequilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita et al., Nature (London) 440, 900 (2006)10.1038/nature04693].

Subfields: Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/f6098539a0d625c0dc25c5b289f7c222c54e946b

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Citations in the corpus

Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians (2019, background): “Two well-known instances are integrable systems [13, 14] and the manybody localized (MBL) phase [15–18], both of which avoid ETH due to the existence of extensively many conserved quantities [19–21].”
Generalized Gibbs ensemble in integrable lattice models (2016, background): “Shortly after the Kinoshita et al experiments, it was shown that, in a system of hardcore bosons far from equilibrium, observables exhibit relaxation to time-independent values that can be predicted by means of a generalized Gibbs ensemble (GGE) [35, 36].”
Dynamics of non-Markovian open quantum systems (2015, background): “…long time limit states resulting from Markovian and non-Markovian evolutions (Markovian evolutions are here understood as 7 In the context of isolated many-body systems, a generalization of the Gibbs state was proposed (Rigol et al., 2007), which is also valid for systems obeying conservation laws.”
Ergodicity breaking transition in finite disordered spin chains (2020, background): “[26] M.”
Quantum quenches in the transverse field Ising chain: II. Stationary state properties (2012, background): “E) [9]. It has been conjectured that the latter arises for integrable models, while the former is obtained for generic systems. Evidence supporting this view has been obtained in a number of examples [9,10,12,13,14,15,16,19,21,22,23]. On the other hand, several numerical studies [24,26,27,37,38] sug”
Quench dynamics and relaxation in isolated integrable quantum spin chains (2016, background): “The maximum entropy principle [163] then suggests that the stationary state density matrix should be given by a GGE [164]”
Quantum quenches in extended systems (2007, methodology): “To quote only a few examples, the models considered include several realizations of one-dimensional (1D) Bose gases [15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], Luttinger liquids [26, 27], coupled 1D condensates [28], strongly correlated 1D fermions”
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): “An exception to the above scenario are integrable systems [64] which equilibrate to a generalised Gibbs ensemble [72, 73].”
One dimensional bosons: From condensed matter systems to ultracold gases (2011, background): “The relevance of the GGE to different 1D integrable systems and fewbody observables, as well as it limits of applicability, have been the subject of several studies during the last years (Barthel and Schollwöck, 2008; Calabrese and Cardy, 2007; Cassidy et al., 2010; Cazalilla, 2006; Cramer et al., ”
Quantum quenches in integrable field theories (2009, background): “If the full correctness of equation (41) will be confirmed by future rigorous analysis, it follows that the asymptotic value of the one-point function of a local operator could be computed as an average over a density matrix (14) with a different temperature for each eigenmode: in short, our result ”
Remarks on the notion of quantum integrability (2010, background): “It is thus natural and appealing to generalize the canonical ensemble by the so-called generalized Gibbs ensemble [69],”