Prethermalization and Thermalization in Isolated Quantum Systems

Abstract

Prethermalization has been extensively studied in systems close to integrability. We propose a more general, yet conceptually simpler, setup for this phenomenon. We consider a-possibly nonintegrable-reference dynamics, weakly perturbed so that the perturbation breaks at least one conservation law of the reference dynamics. We argue then that the evolution of the system proceeds via intermediate (generalized) equilibrium states of the reference dynamics. The motion on the manifold of equilibrium states is governed by an autonomous equation, flowing towards global equilibrium in a time of order g −2 , where g is the perturbation strength. We also describe the leading correction to the time-dependent reference equilibrium state, which is, in general, of order g. The theory is well confirmed in numerical calculations of model Hamiltonians, for which we use a numerical linked cluster expansion and full exact diagonalization. arXiv:1810.12320v2 [cond-mat.stat-mech]

Transportless equilibration in isolated many-body quantum systems

“…Closely related further generalizations of the above local equilibration paradigm are the concepts of hindered equilibrium, quasi-equilibrium, metastability, and, above all, prethermalization [1,[32][33][34][35][36]. The first three concepts play a crucial role for instance in chemical reactions with long-lived intermediates, or in quantum systems exhibiting 'glassy behavior' [37,38], while the concept of prethermalization refers, e.g.…”

Slow thermalization of exact quantum many-body scar states under perturbations

“…This aspect is different from the integrable systems where all eigenstates are special and essentially any initial state will show prethermalization. We finally remark that our rigorous bound on the thermalization time does not use Fermi golden rule type arguments that give O(λ −2 ) prethermalization time for nearly integrable systems or when a conservation law is weakly broken [36][37][38]. It is an open question whether such arguments can be extended to the scar thermalization problem.…”

“…Analogously, the deformed scar states in finite sizes are perturbatively related to the exact scar states of the corresponding special Hamiltonian. Moreover, in the thermodynamic limit, a weakly perturbed integrable Hamiltonian prethermalizes to a generalized Gibbs ensemble that persists for a parametrically long timescale [36][37][38], believed to diverge as O(λ −2 ). Similarly, the nonthermal properties of the exact scar states can also survive in quench experiments under perturbations to some parametrically long time even in the thermodynamic limit, which we also expect to diverge as power law in λ in generic cases.…”

Entanglement in a fermion chain under continuous monitoring

“…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][2][3][4], holography [5][6][7], quantum chaos and information scrambling [8,9]. Understanding entanglement is also crucial for designing effective quantum simulators and determining the limits thereof [10][11][12].…”