Thermalization and light cones in a model with weak integrability breaking

Abstract

We employ equation of motion techniques to study the non-equilibrium dynamics in a lattice model of weakly interacting spinless fermions. Our model provides a simple setting for analyzing the effects of weak integrability breaking perturbations on the time evolution after a quantum quench. We establish the accuracy of the method by comparing results at short and intermediate times to timedependent density matrix renormalization group computations. For sufficiently weak integrabilitybreaking interactions we always observe prethermalization plateaux, where local observables relax to non-thermal values at intermediate time scales. At later times a crossover towards thermal behaviour sets in. We determine the associated time scale, which depends on the initial state, the band structure of the non-interacting theory, and the strength of the integrability breaking perturbation. Our method allows us to analyze in some detail the spreading of correlations and in particular the structure of the associated light cones in our model. We find that the interior and exterior of the light cone are separated by an intermediate region, the temporal width of which appears to scale with a universal power-law t 1/3 .

Theory of entropy production in quantum many-body systems

“…This approximation, which is justified in the limit of very weak coupling potentials,V , and very long times (Van Hove limit 78,79 ) amounts to neglecting memory effects in (42). In practice, this works for times after any transient effect or prethermalization plateau [80][81][82] of the isolated system has passed. We then have in this limit…”

Prethermalization and thermalization of a quenched interacting Luttinger liquid

“…Initially, the dynamics of local observables at transient and intermediate time scales are controlled by the corresponding integrable theory serving as a metastable attractor for the non-integrable dynamics [4,27,28]. This trapping in a metastable state has been termed prethermalization [27,29] and is expected to exist for several non-integrable models and models close to integrability [4,27,[30][31][32][33][34][35][36][37][38]. In the quasi-particle picture, prethermalization is associated with the initial formation of well-defined excitations [27] which leads to a dephasing of all terms that are not diagonal in quasi-particle modes, i.e.…”

Quantum kinetic perturbation theory for near-integrable spin chains with weak long-range interactions

“…Accurate and reliable calculations of these phenomena are challenging, at least when going beyond the small system sizes of O(10) where exact diagonalisation (ED) is feasible. Perturbative techniques around the integrable limit suggest themselves for the problem at hand, and various types of such techniques have been employed in the context of prethermalisation, including a flow-equation methods [10], self-consistent mean-field techniques [11], self-consistent time-dependent spin-wave theory [12], and quantum kinetic theory [13][14][15][16]. The notion of quantum kinetic theory subsumes a number of approximate methods based on identifying certain classes of operators (usually those of higher degree in the normal-ordered ladder operators; see section 3 for more precise statements) as negligible, and deriving a reduced set of equations of motion for the remaining operators only [17].…”

“…The notion of quantum kinetic theory subsumes a number of approximate methods based on identifying certain classes of operators (usually those of higher degree in the normal-ordered ladder operators; see section 3 for more precise statements) as negligible, and deriving a reduced set of equations of motion for the remaining operators only [17]. In the abovementioned [13][14][15][16] quantum kinetic theories are developed for studying bosons or fermions in one spatial dimension.…”