Quantum quenches and thermalization in SYK models

Bhattacharya, Ritabrata; Jatkar, Dileep P.; Sorokhaibam, Nilakash

doi:10.1007/jhep07(2019)066

Cited by 43 publications

(40 citation statements)

References 80 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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.…”

Section: Rényi Entropy For Syk and Related Modelsmentioning

confidence: 99%

“…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.…”

Section: Appendix D: Nonequilibrium Field Theory For Rényi Entropy Inmentioning

confidence: 99%

See 1 more Smart Citation

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

Haldar

Bera

Banerjee

2020

Phys. Rev. Research

View full text Add to dashboard Cite

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.

show abstract

Section: Rényi Entropy For Syk and Related Modelsmentioning

confidence: 99%

Section: Appendix D: Nonequilibrium Field Theory For Rényi Entropy Inmentioning

confidence: 99%

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

Haldar

Bera

Banerjee

2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…For this condition to also be sufficient, we need to show that the formal solution of Φ given by (15) indeed yields the desired asymptotic behavior in the limit ϵ → 0. To examine this, we can again substitute (33) in (34) and then in (15), and finally take the ϵ → 0 limit. This yields…”

Section: Time Reparametrizationmentioning

confidence: 99%

“…This peculiarity is due to the noncausal nature of the event horizon on which the dilaton is evaluated. Finally, we note that quantum quenches in SYK model have been studied in [33,34]. However, we consider different types of deformations here.…”

Section: A Typical Pumped State In Nads 2 Holographymentioning

confidence: 99%

Time-dependent NAdS2 holography with applications

2020

View full text Add to dashboard Cite

We develop a method for obtaining exact time-dependent solutions in Jackiw-Teitelboim gravity coupled to nonconformal matter and study consequences for NAdS 2 holography. We study holographic quenches in which we find that the black hole mass increases. A semiholographic model composed of an infrared NAdS 2 holographic sector representing the mutual strong interactions of trapped impurities confined at a spatial point is proposed. The holographic sector couples to the position of a displaced impurity acting as a self-consistent boundary source. This effective 0 þ 1-dimensional description has a total conserved energy. Irrespective of the initial velocity of the particle, the black hole mass initially increases, but after the horizon runs away to infinity in the physical patch, the mass vanishes in the long run. The total energy is completely transferred to the kinetic energy or the self-consistent confining potential energy of the impurity. For initial velocities below a critical value determined by the mutual coupling, the black hole mass changes sign in finite time. Above this critical velocity, the initial condition of the particle can be retrieved from the SLð2; RÞ invariant exponent that governs the exponential growth of the bulk gravitational SLð2; RÞ charges at late time.

show abstract

“…The scaling laws mentioned above can not be explained by the usual Kibble-Zurek scaling [25,26], unlike that in integrable or weakly-integrable models [20][21][22][23][24]. Although, there have been a few studies on non-equilibrium dynamics of the original SYK model [27][28][29][30], none of them addressed the issue of a quench across a non-trivial QPT.As described schematically in fig.1, we study a time (t)dependent version of the model in ref. [6], H(t) = H c + arXiv:1903.09652v2 [cond-mat.str-el] 30 Sep 2019 2 quenching i n c r e a s i n g t i m e decoupled system critical pt.…”

mentioning

confidence: 99%

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

Haldar

Bera

et al. 2020

Phys. Rev. Research

View full text Add to dashboard Cite

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...

show abstract

Quantum quenches and thermalization in SYK models

Cited by 43 publications

References 80 publications

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

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

Time-dependent NAdS2 holography with applications

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

Contact Info

Product

Resources

About