Thickening and sickening the SYK model

Khveshchenko, D. V.

doi:10.21468/scipostphys.5.1.012

Cited by 28 publications

(24 citation statements)

References 99 publications

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“…At low-energies, the complex SYK model realizes a compressible, gapless phase [53,55] without any long-lived quasiparticles. A number of recent works have studied the transport properties associated with higher dimensional lattice generalizations of SYK islands with strong disorder [56,57,58,59,60,61,62,63,64,65]. The model defined in Eq.…”

Section: A Solvable Limitmentioning

confidence: 99%

The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids

Chowdhury

Berg

2020

Annals of Physics

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The paradigmatic Migdal-Eliashberg theory of the electron-phonon problem is central to the understanding of superconductivity in conventional metals. This powerful framework is justified by the smallness of the Debye frequency relative to the Fermi energy, and allows an enormous simplification of the full manybody problem. However, superconductivity is found also in many families of strongly-correlated materials, in which there is no a priori justification for the applicability of Eliashberg theory. In these systems, superconductivity emerges out of an anomalous metallic state, calling for a new theoretical framework to describe pairing out of a non-Fermi liquid. In this article, we review two model systems in which such behavior is found: a Fermi sea coupled to gapless bosonic fluctuations, and a system of fermions with local, strongly frustrated interactions. In both models, there is a well-defined limit in which the Eliashberg equations are asymptotically exact even in the strongly coupled regime. These models thus provide tractable examples of how superconductivity can emerge in the absence of coherent electronic quasiparticles; they also demonstrate the surprisingly wide applicability of the Eliashberg formalism, well beyond the conventional regime for which it was originally designed.

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Section: A Solvable Limitmentioning

confidence: 99%

The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids

Chowdhury

Berg

2020

Annals of Physics

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“…The issue of chaotic to non-chaotic transiton is considered with several different generalization of the SYK models [52][53][54][55][56]. Among all these generalizations, the non-Fermi Liquid phases given by the SYK-type models all possess a maximal chaotic behavior and Lyapunov exponent saturating to 2π/β, with only one exception that contains time dependent interaction [3,57].…”

Section: Jhep07(2017)150mentioning

confidence: 99%

Tunable quantum chaos in the Sachdev-Ye-Kitaev model coupled to a thermal bath

Chen

Zhai

Zhang

2017

J. High Energ. Phys.

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The Sachdev-Ye-Kitaev (SYK) model describes Majorana fermions with random interaction, which displays many interesting properties such as non-Fermi liquid behavior, quantum chaos, emergent conformal symmetry and holographic duality. Here we consider a SYK model or a chain of SYK models with N Majorana fermion modes coupled to another SYK model with N 2 Majorana fermion modes, in which the latter has many more degrees of freedom and plays the role as a thermal bath. For a single SYK model coupled to the thermal bath, we show that although the Lyapunov exponent is still proportional to temperature, it monotonically decreases from 2π/β (β = 1/(k B T ), T is temperature) to zero as the coupling strength to the thermal bath increases. For a chain of SYK models, when they are uniformly coupled to the thermal bath, we show that the butterfly velocity displays a crossover from a √ T -dependence at relatively high temperature to a linear T -dependence at low temperature, with the crossover temperature also controlled by the coupling strength to the thermal bath. If only the end of the SYK chain is coupled to the thermal bath, the model can introduce a spatial dependence of both the Lyapunov exponent and the butterfly velocity. Our models provide canonical examples for the study of thermalization within chaotic models.

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“…Most recently and closest to our work, [30,31,32] study a chain of SYK clusters coupled by (random and non-random) quadratic links; although the starting point does not have a Fermi surface, the resulting states of matter may be closely related to ours. Studies of higher-dimensional generalizations of the SYK model, with various motivations, include [33,34,35,36,37,38,39,40]. In particular, [40] realizes a bosonic analog of the semi-holographic construction using SYK chains.…”

Section: Introductionmentioning

confidence: 99%

Strange metal from local quantum chaos

Ben-Zion

McGreevy

2018

Phys. Rev. B

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How to make a model of a non-Fermi-liquid metal with efficient current dissipation is a long-standing problem. Results from holographic duality suggest a framework where local critical fermionic degrees of freedom provide both a source of decoherence for the Landau quasiparticle, and a sink for its momentum. This leads us to study a Kondo lattice type model with SYK models in place of the spin impurities. We find evidence for a stable phase at intermediate couplings.1 For a review of the large literature, see [1]. 2 For a more leisurely discussion of these issues, see also §5 of [7].The model is a rather direct and crude discretization of the AdS 2 × R d near-horizon

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Thickening and sickening the SYK model

Cited by 28 publications

References 99 publications

The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids

The unreasonable effectiveness of Eliashberg theory for pairing of non-Fermi liquids

Tunable quantum chaos in the Sachdev-Ye-Kitaev model coupled to a thermal bath

Strange metal from local quantum chaos

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