Memory-preserving equilibration after a quantum quench in a one-dimensional critical model

Abstract

One of the fundamental principles of statistical physics is that only partial information about a system's state is required for its macroscopic description. This is not only true for thermal ensembles, but also for the unconventional ensemble, known as Generalized Gibbs Ensemble (GGE), that is expected to describe the relaxation of integrable systems after a quantum quench. By analytically studying the quench dynamics in a prototypical one-dimensional critical model, the massless free bosonic field theory, we find evidence of a novel type of equilibration characterized by the preservation of an enormous amount of memory of the initial state that is accessible by local measurements. In particular, we show that the equilibration retains memory of non-Gaussian initial correlations, in contrast to the case of massive free evolution which erases all such memory. The GGE in its standard form, being a Gaussian ensemble, fails to predict correctly the equilibrium values of local observables, unless the initial state is Gaussian itself. Our findings show that the equilibration of a broad class of quenches whose evolution is described by Luttinger liquid theory with an initial state that is non-Gaussian in terms of the bosonic field, is not correctly captured by the corresponding bosonic GGE, raising doubts about the validity of the latter in general onedimensional gapless integrable systems such as the Lieb-Liniger model. We also propose that the same experiment by which the GGE was recently observed [Langen et al., Science 348 (2015) 207-211] can also be used to observe its failure, simply by starting from a non-Gaussian initial state.Introduction -Understanding the physics of quantum many-body systems out of equilibrium is one of the most challenging open problems today [1,2]. Of central interest is the problem of quantum quenches i.e. abrupt changes of the Hamiltonian parameters of a closed quantum system [3], especially in one-dimensional (1d) integrable systems where the study of quantum dynamics has led to intriguing discoveries, like the experimental observation of lack of thermalization [4] and the theoretical prediction of the Generalized Gibbs Ensemble (GGE) [5] which has recently been observed experimentally [6]. The GGE is expected to describe the equilibration of local observables after a quantum quench in an integrable system by taking into account all constraints associated to its conserved charges [3,5,. While in its standard form it was constructed exclusively out of local conserved charges [28,29], it has been recently shown that quasi-local charges must also be included [46][47][48][49][50][51][52][53][54][55][56][57][58][59][60]. This gives an answer to the fundamental question of how much information about the initial state survives in the final values of local observables. Other aspects of interest are the asymptotic behavior towards equilibrium [13,30,34,41,61] or the restoration of symmetries of the post-quench Hamiltonian that are absent in the initial state [62,63].

Entanglement Spreading in a Minimal Model of Maximal Many-Body Quantum Chaos

“…Indeed, for generic values of θ and φ the states are not Gaussian in terms of the time evolving fermions and this makes the problem analytically untreatable. Moreover, since the dispersion is linear, the usual arguments about Gaussification do not apply [74,75]. Interestingly, not even separating states are always Gaussian: transverse separating states are Gaussian only for φ i = 0, π [76].…”

Quantum quenches in free field theory: universal scaling at any rate

“…(1.5) diverges as δt → 0. This result appears paradoxical at first sight, since at least in low dimensions, there are perfectly reasonable results for truly instantaneous quenches [25][26][27][28][29]. This issue was examined in detail in [22] by considering UV finite quantities, such as correlation functions at finite spatial separations and the excess energy produced.…”

Integrability-Protected Adiabatic Reversibility in Quantum Spin Chains

“…The presence of an extensive set of integral of motions suggests that the generalised Gibbs ensemble (GGE) Ô GGE = Tr[Ô e − j λjQj ]/Z has to be used in place of the standard one [20,21], where the appropriate set of charges has been accurately characterized in several studies [22][23][24][25][26]. The validity of the GGE conjecture has been nowadays extensively verified not only on the theoretical ground [12,13,[30][31][32][33][34][35][36][37][38][39][40][41][42], but even on the experimental side [5,43].Beyond quantum quenches, integrability constraints can be engineered to induce exotic out-of-equilibrium properties, including superdiffusive transport [44][45][46][47][48][49][50][51][52][53][54][55], dynamical ordering [26,56] and efficient heat pumps [57,58]. In this context, generalized hydrodynamics [59,60] (see also ) has provided a unifying framework to accurately describe integrable systems in the quasi-stationary regime which emerges from inhomogeneous initial conditions.In this letter we consider the out-of-equilibrium dynamics of the spin-1/2 XXZ chain Hamiltonian in the presence of a non-vanish...…”