Strongly Correlated Metal Built from Sachdev-Ye-Kitaev Models

Abstract

Prominent systems like the high-T_{c} cuprates and heavy fermions display intriguing features going beyond the quasiparticle description. The Sachdev-Ye-Kitaev (SYK) model describes a (0+1)D quantum cluster with random all-to-all four-fermion interactions among N fermion modes which becomes exactly solvable as N→∞, exhibiting a zero-dimensional non-Fermi-liquid with emergent conformal symmetry and complete absence of quasiparticles. Here we study a lattice of complex-fermion SYK dots with random intersite quadratic hopping. Combining the imaginary time path integral with real time path integral formulation, we obtain a heavy Fermi liquid to incoherent metal crossover in full detail, including thermodynamics, low temperature Landau quasiparticle interactions, and both electrical and thermal conductivity at all scales. We find linear in temperature resistivity in the incoherent regime, and a Lorentz ratio L≡(κρ/T) varies between two universal values as a function of temperature. Our work exemplifies an analytically controlled study of a strongly correlated metal.

Dispersive Sachdev-Ye-Kitaev model: Band structure and quantum chaos

“…This expression is consistent with the result by expanding the effective action in 30 and D r is proportional to ω in low-energy limit. There are also contributions from c∂ t c and constant hopping t. Since we are interested in lowenergy behavior, we approximate the current operator by the low-energy version:…”

“…From spectral function, (for a tight-binding chain with hopping strength t and for simplicity we only consider the result for µ = 0 in this section, where the charge transport decouples from the energy transport. 30,36 ) it says that the retarded Green's function for charge density correlator Π R,nn (p, ω) = −i dtdx e iωt−ikx θ(t) [n(x, t), n(0, 0)] contains two poles for t ω, p, T :…”

“…Following the basic construction of SYK model, many different generalizations is proposed to extend our knowledge of non-Fermi Liquid, quantum chaos and holographic duality . One important strategy is to couple different quantum dots (with SYK interaction or not) to get a model in higher dimension or study the transition (or crossover) between different fixed points [30][31][32][33][34][35][36][37] . In 30 , the authors study a lattice of complex fermion version of SYK models with intra cell random interaction and inter cell random hopping:…”

“…By a naive power counting, the low-energy physics is dominated by the random hopping (in 30 they call this a heavy Fermi-Liquid) and for small V /J there should be a crossover to the fixed point of weakly coupled SYK models (they call this an incoherent metal) when we increase the temperature. They study this crossover by calculating spectral function, entropy and transport coefficients including charge diffusive constant.…”

Universality and Thouless energy in the supersymmetric Sachdev-Ye-Kitaev model

“…Recently, different extensions of the SYK model have been studied including several fermionic flavors [42,43], higher dimensions [44][45][46][47][48], one plus two-body interactions [49][50][51], with supersymmetry [52][53][54][55][56][57][58][59] and with no disorder [37,60,61].…”