Quantum quench of the Sachdev-Ye-Kitaev model

Eberlein, Andreas; Kasper, Valentin; Sachdev, Subir; Steinberg, Julia

doi:10.1103/physrevb.96.205123

Cited by 122 publications

(160 citation statements)

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“…Interacting Sachdev-Ye-Kitaev models (SYK 4 ), for example, contain correlated pair hopping terms of random strengths. The relaxation dynamics and level spacing statistics of SYK 4 models have been studied recently [92,[148][149][150]. However, these models have no spatial structure, so there are no transport/spreading effects.…”

Section: Discussion and Contextmentioning

confidence: 99%

Dynamics and level statistics of interacting fermions in the lowest Landau level

et al. 2018

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We consider the unitary dynamics of interacting fermions in the lowest Landau level, on spherical and toroidal geometries. The dynamics are driven by the interaction Hamiltonian which, viewed in the basis of single-particle Landau orbitals, contains correlated pair hopping terms in addition to static repulsion. This setting and this type of Hamiltonian has a significant history in numerical studies of fractional quantum Hall (FQH) physics, but the many-body quantum dynamics generated by such correlated hopping has not been explored in detail. We focus on initial states containing all the fermions in one block of orbitals. We characterize in detail how the fermionic liquid spreads out starting from such a state. We identify and explain differences with regular (single-particle) hopping Hamiltonians. Such differences are seen, e.g.in the entanglement dynamics, in that some initial block states are frozen or near-frozen, and in density gradients persisting in long-time equilibrated states. Examining the level spacing statistics, we show that the most common Hamiltonians used in FQH physics are not integrable, and explain that GOE statistics (level statistics corresponding to the Gaussian orthogonal ensemble) can appear in many cases despite the lack of time-reversal symmetry.

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Section: Discussion and Contextmentioning

confidence: 99%

Dynamics and level statistics of interacting fermions in the lowest Landau level

et al. 2018

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“…For our purposes we chose a typical grid-size of the t 1 − t 2 plane of 8000 × 8000 and set δ = 10 −8 . The initial conditions are found by iterating the SDE in frequency space [32,37].…”

Section: Supplemental Materialmentioning

confidence: 99%

“…Grey lines denote the free Green's function, G 0 ; black lines the disorder averaged full Green's function, G(t, t ) = −i T C {c i (t)c † j (t )} (where T C denotes contour time ordering); and dotted lines represent disorder averages of K ij and J ij;kl , respectively. The precise form of our KBE's is read off from the diagrams to be(2) As initial conditions we fix the Green's function in the lower quadrant of the two-time plane (t, t ) with low temperature initial states, that are determined by numerically iterating the equilibrium Schwinger-Dyson equations [32,36,37].We then switch on the drive at time t = 0 and follow the evolution of the system. The resulting equations are integrated numerically employing a predictor-corrector scheme; see supplementary material for details [38].…”

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confidence: 99%

Periodically Driven Sachdev-Ye-Kitaev Models

Kuhlenkamp

Knap

2020

Phys. Rev. Lett.

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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...

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“…A recent study addressed these matters directly in a zero-density 1 þ 1D CFT relating the Vaidya shell to structure realized in the large central charge limit [22,23], suggesting that the instantaneous thermalization might be a large N artifact. Another recent study addressed thermalization of fermionic Green's functions after a quench in the Sachdev-Ye-Kitaev model [24], which is believed to be a quantum system with a holographic dual. For q-fermion interactions with q → ∞, instantaneous thermalization was also found, consistent with an AdS 2 -Vaidya dual.…”

Section: Introductionmentioning

confidence: 99%

Holography and thermalization in optical pump-probe spectroscopy

Bagrov¹,

Craps

Galli

et al. 2018

Phys. Rev. D

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Using holography, we model experiments in which a 2 þ 1D strange metal is pumped by a laser pulse into a highly excited state, after which the time evolution of the optical conductivity is probed. We consider a finite-density state with mildly broken translation invariance and excite it by oscillating electric field pulses. At zero density, the optical conductivity would assume its thermalized value immediately after the pumping has ended. At finite density, pulses with significant dc components give rise to slow exponential relaxation, governed by a vector quasinormal mode. In contrast, for high-frequency pulses the amplitude of the quasinormal mode is strongly suppressed, so that the optical conductivity assumes its thermalized value effectively instantaneously. This surprising prediction may provide a stimulus for taking up the challenge to realize these experiments in the laboratory. Such experiments would test a crucial open question faced by applied holography: are its predictions artifacts of the large N limit or do they enjoy sufficient UV independence to hold at least qualitatively in real-world systems?

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Quantum quench of the Sachdev-Ye-Kitaev model

Cited by 122 publications

References 35 publications

Dynamics and level statistics of interacting fermions in the lowest Landau level

Dynamics and level statistics of interacting fermions in the lowest Landau level

Periodically Driven Sachdev-Ye-Kitaev Models

Holography and thermalization in optical pump-probe spectroscopy

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