Periodically Driven Sachdev-Ye-Kitaev Models

Abstract

Periodically driven quantum matter can realize exotic dynamical phases. In order to understand how ubiquitous and robust these phases are, it is pertinent to investigate the heating dynamics of generic interacting quantum systems. Here we study the thermalization in a periodically-driven generalized Sachdev-Ye-Kitaev (SYK)-model, which realizes a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) at a tunable energy scale. Developing an exact field theoretic approach, we determine two distinct regimes in the heating dynamics. While the NFL heats exponentially and thermalizes rapidly, we report that the presence of quasi-particles in the heavy FL obstructs heating and thermalization over comparatively long time scales. Prethermal high-frequency dynamics and possible experimental realizations of non-equilibrium SYK physics are discussed as well.Coherent periodic driving emerges as a fascinating new tool to induce novel properties both in synthetic quantum systems and in solid state. Examples include the manipulation of topological Band structures [1][2][3][4][5][6][7][8], the realization of light-induced ordered states [9][10][11][12][13][14][15], and driving dynamical transitions from many-body localized to ergodic phases [16][17][18][19]. While it may be possible to stabilize such exotic driven quantum states in an intermediate prethermal regime [20][21][22][23][24] or by adding disorder [16], the generic fate of an isolated periodically driven system is that it absorbs energy from the drive and heats toward an infinite temperature state, provided that the driving frequency is low enough [25]. By contrast, for high driving frequency this absorption is inefficient as it requires large rearrangements in the many-body state [24,26,27]. To elucidate this interplay, it would be valuable to find a model that captures the effect of strong interactions yet can be solved in the thermodynamic limit.In this work, we propose that the generalized Sachde-Ye-Kitaev (SYK-) model [28,29] is a prototypical model for fast heating in periodically driven quantum systems. The SYK model has been originally introduced as a solvable model for a non-Fermi liquid [28,30]. Recently, work initiated by Kitaev [29,[31][32][33] studied quantum dynamics, chaos, and information scrambling in the SYK model and showed that it saturates bounds for the operator growth in out-of-time ordered correlation functions [32]. Remarkably, generalizations of SYK models feature a crossover from a heavy Fermi liquid (FL) to a non-Fermi liquid (NFL) and can be solved exactly [34]. By periodically driving these models we study the heating dynamics of a heavy FL and a NFL in the thermodynamic limit, see Fig. 1 for an illustration. While we find the NFL to rapidly thermalize, the existence of well-defined quasi particles dramatically slows down the full thermalization of the heavy FL. Furthermore, heating can be suppressed in both cases by driving with sufficiently high frequencies.The system then enters a prethermal regime characterized by an effe...

More on complex Sachdev-Ye-Kitaev eternal wormholes

“…The quench dynamics of SYK-like models can be studied using the Keldysh approach [38][39][40][41][42]. We firstly define several real-time Green's functions G > and G < :…”

“…We then evolve the Green's function step by step using the standard numerical method by discretizing G ≷ (u 1 , u 2 ) into large matrices [38][39][40][41][42]. The numerical results for G > (u 1 , u 2 ) are shown in figure 5.…”

Subsystem Rényi entropy of thermal ensembles for SYK-like models

“…The hallmark of these models is that the computation of correlation functions is reduced to integral equations in the large-N limit. This also leads to the ability to compute quantum dynamics precisely [49][50][51][52][53].…”

Rényi entanglement entropy of Fermi and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories

“…Remarkably, these models can be solved exactly in a suitable large-N limit, without resorting to any kind of perturbative treatment. As a result, the study of this family of large-N fermionic model has given insights into transport [32,[43][44][45][46][47], thermalization [54][55][56][57][58][59][60][61][62], many-body chaos [27,30,34], and entanglement [43,[63][64][65][66][67] in strongly interacting fermionic systems, as well as their intriguing connections with black holes [27,28,35]. Here we use the path-integral technique of Sec.…”

“…II D for SYK model and its extensions allows us to access ground-state entanglement in these large-N model. In this section, we discuss the large-N Schwinger-Keldysh formulation, which will enable us to track the time evolution of entanglement entropy under nonequilibrium situations [54][55][56][57][58][59][60][61][62]. We demonstrate this by deriving the Swinger-Keldysh action and saddle-point equations for outof-equilibrium evolution in the SYK q model [Eq.…”