Quantum quenches in a holographic Kondo model

Abstract

We study non-equilibrium dynamics and quantum quenches in a recent gauge/ gravity duality model for a strongly coupled system interacting with a magnetic impurity with SU(N ) spin. At large N , it is convenient to write the impurity spin as a bilinear in Abrikosov fermions. The model describes an RG flow triggered by the marginally relevant Kondo operator. There is a phase transition at a critical temperature, below which an operator condenses which involves both an electron and an Abrikosov fermion field. This corresponds to a holographic superconductor in AdS 2 and models the impurity screening. We quench the Kondo coupling either by a Gaussian pulse or by a hyperbolic tangent, the latter taking the system from the condensed to the uncondensed phase or vice-versa. We study the time dependence of the condensate induced by this quench. The timescale for equilibration is generically given by the leading quasinormal mode of the dual gravity model. This mode also governs the formation of the screening cloud, which is obtained as the decrease of impurity degrees of freedom with time. In the condensed phase, the leading quasinormal mode is imaginary and the relaxation of the condensate is over-damped. For quenches whose final state is close to the critical point of the large N phase transition, we study the critical slowing down and obtain the combination of critical exponents zν = 1. When the final state is exactly at the phase transition, we find that the exponential ringing of the quasinormal modes is replaced by a power-law behaviour of the form ∼ t −a sin(b log t). This indicates the emergence of a discrete scale invariance.

Quantum quenches and thermalization in SYK models

“…Longer time interval only injects more energy into the system resulting in higher final temperature. (a) Once both the time arguments are outside the quench region, we find that the greater Green's function thermalizes rapidly but not instantaneously, as can be seen in Figure (6). Figure (7a, 7b) are two resolved plots of G > (t − 100, t) for different initial inverse temperatures as a function of t for step quenches.…”

“…We also used a fixed time step size dt = 0.05. 6 In the rest of the paper, we will suppress factors of this time step size dt. So, unless it is explicitly mentioned all the times are measured in units of dt.…”

“…The study of non-equilibrium dynamics is becoming important both in condensed matter physics [1][2][3][4][5][6][7][8][9] as well as in string theory [10][11][12][13][14]. One of the most interesting question in this field is to understand patterns of thermalization in the systems which are out of equilibrium.…”

Time evolution of entanglement for holographic steady state formation

“…26 For this type of problem, there is a so-called entropy condition. This is a requirement that characteristic lines of the differential operator involved, i.e.…”

“…An example of such a solution was found in [95] in the limit of large dimensions d → ∞. However, obtaining a clear, numerical shock-rarefaction solution 26 In full generality, the Riemann problem is a initial value problem for a non-linear PDE with noncontinuous, piecewise-constant initial data. 27 In the characteristic formulation of a PDE, the presence of a shockwave is manifested by the intersection of characteristics.…”