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...

We present a method for calculating Rényi entanglement entropies for fermionic field theories originating from microscopic Hamiltonians. The method builds on an operator identity, which leads to the representation of traces of operator products, and thus Rényi entropies of a subsystem, in terms of fermionic-displacement operators. This allows for a very transparent path-integral formulation, both in and out of equilibrium, having a simple boundary condition on the fermionic fields. The method is validated by reproducing well-known expressions for entanglement entropy in terms of the correlation matrix for noninteracting fermions. We demonstrate the effectiveness of the method by explicitly formulating the field theory for Rényi entropy in a few zero-and higher dimensional large-N interacting models akin to the Sachdev-Ye-Kitaev (SYK) model and for the Hubbard model within the dynamical mean field theory (DMFT) approximation. We use the formulation to compute Rényi entanglement entropy of interacting Fermi liquid (FL) and non-Fermi liquid (NFL) states in the large-N models and compare the results successfully with those obtained via exact diagonalization for finite N. We elucidate the connection between Rényi entanglement entropy and residual entropy of the NFL ground state in the SYK model and extract sharp signatures of quantum phase transition in the entanglement entropy across an NFL to FL transition. Furthermore, we employ the method to obtain nontrivial system-size scaling of entanglement in an interacting diffusive metal described by a chain of SYK dots.

Chaotic quantum systems with Lyapunov exponent λ L obey an upper bound λ L ≤ 2πk B T=ℏ at temperature T, implying a divergence of the bound in the classical limit ℏ → 0. Following this trend, does a quantum system necessarily become "more chaotic" when quantum fluctuations are reduced? Moreover, how do symmetry breaking and associated nontrivial dynamics influence the interplay of quantum mechanics and chaos? We explore these questions by computing λ L ðℏ; TÞ in the quantum spherical p-spin glass model, where ℏ can be continuously varied. We find that quantum fluctuations, in general, make paramagnetic phase less and the replica symmetry-broken spin glass phase more chaotic. We show that the approach to the classical limit could be nontrivial, with nonmonotonic dependence of λ L on ℏ close to the dynamical glass transition temperature T d . Our results in the classical limit (ℏ → 0) naturally describe chaos in supercooled liquid in structural glasses. We find a maximum in λ L ðTÞ substantially above T d , concomitant with the crossover from simple to slow glassy relaxation. We further show that λ L ∼ T α , with the exponent α varying between 2 and 1 from quantum to classical limit, at low temperatures in the spin glass phase.