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

Abstract

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

Electronic spectra with paramagnon fractionalization in the single band Hubbard model

“…In Section II A, we proposed that the primary contribution to the frequency dependence of the electronic self energy arose from an exchange coupling to gapless fractionalized spinons in the second layer of hidden spins produced by fractionalizing the paramagnon; all other fluctuations are gapped out in this theory of pseudogap metal [12,13], apart from those associated with electronic Fermi surface. A marginal Fermi liquid self energy is obtained in such a model if we assume that the spinons are described by a SYK spin liquid [46][47][48], and assume the electronic local density of states is energy independent. Section II A improved on this model by including the energy dependence of the electronic local density of states which is computed in Section IV.…”

“…In the present section we will examine a simple approximation for χ, in which we replace it by the momentum-independent spin susceptibility of the SYK model [46][47][48] χ(q, τ ) ∼ T sin(πT τ ) ;…”

libdlr: Efficient imaginary time calculations using the discrete Lehmann representation

“…First, we demonstrate recovery of the DLR coefficients of a Green's function both from its values on the DLR imaginary time grid and from noisy data on a uniform grid. Second, we demonstrate the process of solving the Dyson equation self-consistently for the Sachdev-Ye-Kitaev model [14][15][16]. All examples are implemented in Fortran; Appendix A contains analogous examples implemented using pydlr.…”

“…As an example, we consider the Dyson equation given by (10) with the Sachdev-Ye-Kitaev (SYK) [14][15][16]…”

Pairing Instabilities of the Yukawa-SYK Models with Controlled Fermion Incoherence

“…In this work, we circumvent such difficulty by examining a variant of the Sachdev-Ye-Kitaev (SYK) model [23][24][25][26][27], so called the Yukawa-SYK model [28][29][30][31], which is exactly solvable and supports non-Fermi liquid ground states. While the previously studied models use the fixed variance of the random coupling, we introduce a continuous distribution of variances.…”