Higher-dimensional Sachdev-Ye-Kitaev non-Fermi liquids at Lifshitz transitions

Haldar, Arijit; Banerjee, Sumilan; Shenoy, Vijay B.

doi:10.1103/physrevb.97.241106

Cited by 60 publications

(64 citation statements)

References 34 publications

(86 reference statements)

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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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“…[37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] involves a single copy of the SYK 'impurity' coupled to a 1d chain of ordinary fermions and pairwise random couplings between the chain and the SYK fermions. Also, a supersymmetric generalization of the SYK model whose spectrum contains two-fermion bound states, alongside the fundamental fermions, was proposed in Ref.…”

Section: Generalized Syk-like Modelsmentioning

confidence: 99%

“…(40,41) may not be simply related to the eigenvalues of any invariant operator, as in the original SYK model [7][8][9][10].…”

Section: Fluctuations About Mean-field Solutionsmentioning

confidence: 99%

Thickening and sickening the SYK model

Khveshchenko

2018

SciPost Phys.

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We discuss higher dimensional generalizations of the 0 + 1-dimensional Sachdev-YeKitaev (SYK) model that has recently become the focus of intensive interdisciplinary studies by, both, the condensed matter and field-theoretical communities. Unlike the previous constructions where multiple SYK copies would be coupled to each other and/or hybridized with itinerant fermions via spatially short-ranged random hopping processes, we study algebraically varying long-range (spatially and/or temporally) correlated random couplings in the general d + 1 dimensions. Such pertinent topics as translationallyinvariant strong-coupling solutions, emergent reparametrization symmetry, effective action for fluctuations, chaotic behavior, and diffusive transport (or a lack thereof) are all addressed. We find that the most appealing properties of the original SYK model that suggest the existence of its 1+1-dimensional holographic gravity dual do not survive the aforementioned generalizations, thus lending no additional support to the hypothetical broad (including 'non-AdS d+2 /non-C F T d+1 ') holographic correspondence.

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“…Since spatial correlation is not built in the original models, these examples contribute to the local non-Fermi liquid [11,12]. Further extension to lattice systems gives rise to a crossover from high-temperature local non-Fermi liquid state to low-temperature Landau Fermi liquid state [13][14][15][16][17][18][19][20]. Now, inspired by the solvability of SYK model and its resultant novel non-Fermi liquid physics, we propose to study a modified periodic Anderson model with SYK-like interaction, which we call Sachdev-Ye-Kitaev periodic Anderson model (SYK-PAM).…”

Section: Introductionmentioning

confidence: 99%

Periodic Anderson model meets Sachdev-Ye-Kitaev interaction: a solvable playground for heavy fermion physics

Zhong

2018

J. Phys. Commun.

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The periodic Anderson model is a classic theoretical model for understanding novel physics in heavy fermion systems. Here, we modify it with the Sachdev-Ye-Kitaev interaction, (random all-to-all interaction) thus the resultant model admits an exact solution at large-N (e.g. spin flavor) limit. By analytical field theory arguments and numerical calculations, we establish that the system supports a low-temperature (heavy) Fermi liquid and more interestingly a non-Fermi liquid solution at elevated temperature/energy. For physical observable, the latter one contributes a sharp peak at Fermi energy for spectral function, a non-Fermi liquid-like T 1 2 resistivity and shows a robust Fano lineshape in tunneling spectrum. This system may be simulated by ultracold atom gases and can serve as a good playground for studying ubiquitous symmetry-breaking instabilities like unconventional superconductivity or topological orders in generic heavy fermion systems.

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Higher-dimensional Sachdev-Ye-Kitaev non-Fermi liquids at Lifshitz transitions

Cited by 60 publications

References 34 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

Thickening and sickening the SYK model

Periodic Anderson model meets Sachdev-Ye-Kitaev interaction: a solvable playground for heavy fermion physics

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