Quenches and (Pre)Thermalisation in a mixed Sachdev-Ye-Kitaev Model

Larzul, Ancel; Schiró, Marco

doi:10.48550/arxiv.2107.07781

Cited by 4 publications

(4 citation statements)

References 34 publications

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“…A Planckian lifetime has also been obtained by nonequilibrium studies of SYK models, which display a recovery of thermal Green's functions in a time that is independent of U , and proportional to the inverse final temperature (Almheiri et al, 2019;Bhattacharya et al, 2019;Dhar et al, 2019;Eberlein et al, 2017a;Kourkoulou and Maldacena, 2017;Lensky and Qi, 2021;Rossini et al, 2020;Samui and Sorokhaibam, 2021;Zhang, 2019); for closely related and complementary insights, see also (Cheipesh et al, 2020;Haldar et al, 2020;Haque and McClarty, 2019;Kuhlenkamp and Knap, 2020;Larzul and Schiró, 2021;Sonner and Vielma, 2017).…”

Section: Non-zero Temperaturesmentioning

confidence: 88%

Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids

Chowdhury,

Georges,

Parcollet

et al. 2021

Preprint

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We present a review of the Sachdev-Ye-Kitaev (SYK) model of compressible quantum many-body systems without quasiparticle excitations, and its connections to various theoretical studies of non-Fermi liquids in condensed matter physics. The review is placed in the context of numerous experimental observations on correlated electron materials. Strong correlations in metals are often associated with their proximity to a Mott transition to an insulator created by the local Coulomb repulsion between the electrons. We explore the phase diagrams of a number of models of such local electronic correlation, employing a dynamical mean field theory in the presence of random spin exchange interactions. Numerical analyses and analytical solutions, using renormalization group methods and expansions in large spin degeneracy, lead to critical regions which display SYK physics. The models studied include the single-band Hubbard model, the t-J model and the two-band Kondo-Heisenberg model in the presence of random spin exchange interactions. We also examine non-Fermi liquids obtained by considering each SYK model with random four-fermion interactions to be a multi-orbital atom, with the SYK-atoms arranged in an infinite lattice. We connect to theories of sharp Fermi surfaces without any low-energy quasiparticles in the absence of spatial disorder, obtained by coupling a Fermi liquid to a gapless boson; a systematic large N theory of such a critical Fermi surface, with SYK characteristics, is obtained by averaging over an ensemble

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Section: Non-zero Temperaturesmentioning

confidence: 88%

Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids

Chowdhury,

Georges,

Parcollet

et al. 2021

Preprint

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“…In particular, one expects the subsystem entanglement entropy to saturate to the thermal entropy at this effective temperature. Several studies have characterized such non-equilibrium dynamics of the SYK model and its variants [27][28][29][30][31][32][33][34][35][36][37][38]. Of particular interest for us is the surprising result of [28], in which the authors studied an SYK chain formed by coupling SYK dots with random two-body interaction in the large-N limit [15].…”

Section: Introductionmentioning

confidence: 99%

Thermalization of randomly coupled SYK models

Sohal¹,

Nie²,

Sun³

et al. 2022

J. Stat. Mech.

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We investigate the thermalization of Sachdev–Ye–Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large-N limit. Using numerical large-N methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large-N artifact by repeating the quench for finite N and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the N → ∞ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations.

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Section: Introductionmentioning

confidence: 99%

Thermalization of Randomly Coupled SYK Models

Sohal,

Nie,

Sun

et al. 2021

Preprint

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We investigate the thermalization of Sachdev-Ye-Kitaev (SYK) models coupled via random interactions following quenches from the perspective of entanglement. Previous studies have shown that when a system of two SYK models coupled by random two-body terms is quenched from the thermofield double state with sufficiently low effective temperature, the Rényi entropies do not saturate to the expected thermal values in the large-N limit. Using numerical large-N methods, we first show that the Rényi entropies in a pair SYK models coupled by two-body terms can thermalize, if quenched from a state with sufficiently high effective temperature, and hence exhibit state-dependent thermalization. In contrast, SYK models coupled by single-body terms appear to always thermalize. We provide evidence that the subthermal behavior in the former system is likely a large-N artifact by repeating the quench for finite N and finding that the saturation value of the Rényi entropy extrapolates to the expected thermal value in the N → ∞ limit. Finally, as a finer grained measure of thermalization, we compute the late-time spectral form factor of the reduced density matrix after the quench. While a single SYK dot exhibits perfect agreement with random matrix theory, both the quadratically and quartically coupled SYK models exhibit slight deviations.

show abstract

Quenches and (Pre)Thermalisation in a mixed Sachdev-Ye-Kitaev Model

Cited by 4 publications

References 34 publications

Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids

Sachdev-Ye-Kitaev Models and Beyond: A Window into Non-Fermi Liquids

Thermalization of randomly coupled SYK models

Thermalization of Randomly Coupled SYK Models

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