Quench, thermalization, and residual entropy across a non-Fermi liquid to Fermi liquid transition

Abstract

We study the thermalization, after sudden and slow quenches, of an interacting model having a quantum phase transition from a Sachdev-Ye-Kitaev (SYK) non-Fermi liquid (NFL) to a Fermi liquid (FL). The model has SYK fermions coupled to non-interacting lead fermions and can be realized in a graphene flake connected to external leads. A sudden quench to the NFL leads to rapid thermalization via collapse-revival oscillations of the quasiparticle residue of the lead fermions. In contrast, the quench to the FL shows multiple prethermal regimes and much slower thermalization. In the slow quench performed over a time τ , we find that the excitation energy generated has a remarkable intermediate-τ non-analytic power-law dependence, τ −η with η < 1, which seemingly masks the dynamical manifestation of the initial residual entropy of the SYK fermions. Our study gives an explicit demonstration of the intriguing contrasts between the out-of-equilibrium dynamics of a NFL and a FL in terms of their thermalization and approach to adiabaticity.One of the major frontiers in condensed matter physics is to describe gapless phases of interacting fermions without any quasiparticles, namely non Fermi liquids (NFL) [1]. Recently, new insights about fundamental differences between NFLs and Fermi liquids (FL) have been gained in terms of many-body quantum chaos and thermalization. This new impetus has come from exciting developments in a class of NFLs described by Sachdev-Ye-Kitaev (SYK) model, [2][3][4] and its extensions [5][6][7][8][9][10][11][12][13], and their connections with black holes in quantum gravity [3,14,15]. In particular, the model proposed in ref. [6] classifies the SYK NFL and a FL as two distinct chaotic fixed points, separated by a quantum phase transition (QPT). In this characterization, the NFL thermalizes much faster than the FL, as quantified by a rate of the onset of chaos or the Lyapunov exponent [3,6,16].However, the Lyapunov exponent is computed from an equilibrium dynamical correlation, the so-called outof-time-ordered correlator [3,4,17]. Here, using the model of ref.[6] as a template, we ask whether such contrast between the NFL and FL persists even for thermalization from a completely out-of-equilibrium situation, e.g. a quantum quench. Remarkably, the exactly solvable nature of the model allows us to study its full nonequilibrium evolution exactly. By using non-equilibrium Keldysh field theory in the thermodynamic limit, as well as numerical exact diagonalization (ED) for finite systems, we demonstrate a drastic difference in thermalization rates for the NFL and FL after a sudden quench. Furthermore, the Landau description of a FL is based on the concept of adiabatic time evolution from a noninteracting system under slow switching on of the interaction, without encountering a phase transition. Is it possible to evolve an NFL adiabatically to the FL and vice versa? We argue that such evolution is not possible here due to another intriguing aspect of the SYK NFL, namely the finite zero-temperature residual e...

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

“…II D 5. The results for higher order Rényi entropies and time evolution of Rényi entropy in nonequilibrium situations will be communicated in a future work [71].…”

“…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.…”

“…III for all the models discussed in this section by numerically solving the saddlepoint equations, such as Eqs. (67) and (71), and using Eq. (69).…”

“…7(d), the coefficient of the growth function changes with interaction strength. These aspects will be studied in detail in a future work [71].…”

“…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.…”