Abstract

Inspired by the recent interest in the Sachdev–Ye–Kitaev (SYK) model, we study a class of multi-flavored one- and two-band fermion systems with no bare dispersion. In contrast to the previous work on the SYK model that would routinely assume spatial locality, thus unequivocally arriving at the so-called ‘locally-critical’ scenario, we seek to attain a spatially-dispersing ‘globally-SYK’ behavior. To that end, a variety of the Lorentz-(non)invariant space-and/or-time dependent algebraically decaying interaction functions is considered and some of the thermodynamic and transport properties of such systems are discussed.

Highlights

  • The recent rise of the asymptotically solvable 0 + 1-dimensional SYK model [1,2,3,4] possessing a genuine holographic dual has rekindled the long-standing interest in analytically solvable examples of non-Fermi liquid (NFL) behavior

  • All those works operated under the common assumption of a spatially local nature of the SYK propagator which limitation resulted in a number of the NFL scenarios exhibiting ‘(ultra-)local’ criticality characterized by the lack of any spatial dispersion

  • It would seem that a firm justification of the general holographic approach as a viable phenomenological scheme should require one to venture off the beaten path by attempting to extend it to the multitude of more general, including spatially dispersing, NFLs

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Summary

Introduction

The recent rise of the asymptotically solvable 0 + 1-dimensional SYK model [1,2,3,4] possessing a genuine (albeit, still debated over its fine details) holographic dual has rekindled the long-standing interest in analytically solvable examples of non-Fermi liquid (NFL) behavior. The pertinent interaction functions—-which play the role of disorder correlations in the (generalized) SYK models [2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]—could be distinguished on the basis of such important properties as their short- vs long-ranged nature, combined vs independent dependence on space-time separation, etc Depending on such important details, the systems in question might demonstrate an entire variety of novel (non)critical regimes. As the SYK-related examples show, the key requirement that enables asymptotically exact solutions of such systems—as well as their non-random counterparts [27,28,29,30]—is a large number N of the different species (see, Equation (6) below for a further clarification)

Results
Schwinger–Dyson Equations and Their Solutions
Hybrid Models
Conclusions
Full Text
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