Universal aspects of thermalization after a quantum quench

Tatsuhiko N. Ikeda, Yu Watanabe

Surbhi Khetrapal

In this thesis we study the time dependence of correlators such as Green function, entanglement (Renyi) entropy and mutual information following quantum quench in Conformal Field Theories (CFTs) and their holographic duals (AdS). We develop a new recursive method to analytically study the thermalization of retarded Green function in CFTs holographically dual to thin shell AdS Vaidya space times. Using this method, analytic results for short time thermalization of the Green function are obtained; its long time behaviour is obtained by implementing this method numerically. This method is also used to study the late time behaviour of the minimally coupled scalar in AdS3 Vaidya and the shear vector mode in AdS5 Vaidya. Studying the latter, we obtain the universal ratio of the shear viscosity to entropy density from a time dependent process. We study the time evolution of single interval Renyi and entanglement entropies following local quantum quenches in CFTs at finite temperature for which the locally excited states have a finite temporal width. We show that the time dependence of Renyi and entanglement entropies, at second order in width, is universal and is determined by the expectation value of the stress tensor in the replica geometry. We study local quenches in two dimensional CFT at large central charge by operators carrying higher spin charge. The holographic description is used to obtain the single interval entanglement entropy, mutual information and scrambling time following the quench. We find that the change in entanglement entropy is finite (and real) only if the spin-three charge, q, is bounded by the energy of the perturbation, E, as |q|/c < E^2/c^2. For larger values of the spin-three charge, the scrambling time is shorter than for pure gravity and controlled by the spin-three Lyapunov exponent.

Suchetan Das, Bobby Ezhuthachan, Arnab Kundu +2 more

Abstract In this article, we explore dynamical aspects of Out-of-Time-Order correlators (OTOCs) for critical quenches, in which an initial non-trivial state evolves with a CFT-Hamiltonian. At sufficiently large time, global critical quenches exhibit a universal thermal-behavior in terms of low-point correlators. We demonstrate that, under such a quench, OTOCs demarcate chaotic CFTs from integrable CFTs by exhibiting a characteristic exponential Lyapunov growth for the former. Upon perturbatively introducing inhomogeneity to the global quench, we further argue and demonstrate with examples that, such a perturbation parameter can induce a parametrically large scrambling time, even for a CFT with an order one central charge. This feature may be relevant in designing measurement protocols for non-trivial OTOCs, in general. Both our global and inhomogeneous quench results bode well for an upper bound on the corresponding Lyapunov exponent, that may hold outside thermal equilibrium.

Marcos Rigol

Anatoli Polkovnikov, K. Sengupta, Alessandro Silva +1 more

This Colloquium gives an overview of recent theoretical and experimental progress in the area of nonequilibrium dynamics of isolated quantum systems. There is particularly a focus on quantum quenches: the temporal evolution following a sudden or slow change of the coupling constants of the system Hamiltonian. Several aspects of the slow dynamics in driven systems are discussed and the universality of such dynamics in gapless systems with specific focus on dynamics near continuous quantum phase transitions is emphasized. Recent progress on understanding thermalization in closed systems through the eigenstate thermalization hypothesis is also reviewed and relaxation in integrable systems is discussed. Finally key experiments probing quantum dynamics in cold atom systems are overviewed and put into the context of our current theoretical understanding.

Smitha Vishveshwara, Aashish A. Clerk, P. Nalbach