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Abstract We study quantum quenches and subsequent non-equilibrium dynamics of free Dirac fermions in 1 + 1 spacetime dimensions using time dependent mass. The final state is a normalized boundary state which is called generalized Calabrese-Cardy (gCC) state and the system thermalizes to a generalized Gibb’s Ensemble(GGE). We can also tune the initial states so that the final states are exact Calabrese-Cardy (CC) state and special gCC states. The system in the CC state thermalizes to a Gibb’s ensemble. We derive closed-form analytic expressions for the growth of entanglement entropy of subsystems consisting of arbitrary number of disjoint intervals in CC state. We show that the entanglement entropy of a single interval grows monotonically before saturation. In case of certain gCC states, for particular charges, the entanglement entropy of a single interval grows non-monotonically when the effective chemical potential is increased beyond a critical value. We argue that the non-monotonic growth of entanglement entropy is a boundary effect which arises due to increase in long range correlation and decrease in short range correlation at early times.

Abstract We study thermalization of charged SYK model in two different phases. We show that both the highly chaotic liquid phase and the dilute gas phase thermalize. Surprisingly the dilute gas state thermalizes instantaneously. We argue that this phenomenon arises because the system in this phase consists of only long-lived quasi-particles at very low density. The liquid state thermalizes exponentially fast. We also show that the additional introduction of random mass deformation (q = 2 SYK term) slows down thermalization but the system thermalizes exponentially fast. This is observed despite the fact that the addition of large q = 2 SYK interaction forces spectral statistics to obey Poisson statistics. An interesting new observation is that the effective temperature is non-monotonic during thermalization in the liquid state. It has a bump at relatively long time before settling down to the final value. With non-zero chemical potential, the effective temperature oscillates noticeably before settling down to the final value.

Abstract We study chaotic-integrable transition and the nature of quantum chaos in SYK model with chemical potential. We use a novel numerical technique to calculate the partition function explicitly. We show the phase transition in the presence of large chemical potential. We also show that a mass-like term consisting of two fermion random interaction (q = 2 SYK term) does not give rise to a sharp transition. We find that turning on the chemical potential suppresses the Lyapunov exponent in the chaotic phase exponentially.

Abstract We study non-equilibrium dynamics in SYK models using quantum quench. We consider models with two, four, and higher fermion interactions (q = 2, 4, and higher) and use two different types of quench protocol, which we call step and bump quenches. We analyse evolution of fermion two-point functions without long time averaging. We observe that in q = 2 theory the two-point functions do not thermalize. We find thermalization in q = 4 and higher theories without long time averaging. We calculate two different exponents of which one is equal to the coupling and the other is proportional to the final temperature. This result is more robust than thermalization obtained from long time averaging as proposed by the eigenstate thermalization hypothesis(ETH). Thermalization achieved without long time averaging is more akin to mixing than ergodicity.

Abstract We consider quantum quenches in models of free scalars and fermions with a generic time-dependent mass m(t) that goes from m 0 to zero. We prove that, as anticipated in MSS [1], the post-quench dynamics can be described in terms of a state of the generalized Calabrese-Cardy form |ψ〉 = exp[−κ 2 H − ∑ n >2∞ κ n W n ]|Bd〉. The W n (n = 2, 3, . . ., W 2 = H) here represent the conserved W ∞ charges and |Bd〉 represents a conformal boundary state. Our result holds irrespective of whether the pre-quench state is a ground state or a squeezed state, and is proved without recourse to perturbation expansion in the κ n ’s as in MSS. We compute exact time-dependent correlators for some specific quench protocols m(t). The correlators explicitly show thermalization to a generalized Gibbs ensemble (GGE), with inverse temperature β = 4κ 2, and chemical potentials μ n = 4κ n . In case the pre-quench state is a ground state, it is possible to retrieve the exact quench protocol m(t) from the final GGE, by an application of inverse scattering techniques. Another notable result, which we interpret as a UV/IR mixing, is that the long distance and long time (IR) behaviour of some correlators depends crucially on all κ n ’s, although they are highly irrelevant couplings in the usual RG parlance. This indicates subtleties in RG arguments when applied to non-equilibrium dynamics.