Solvable model for quantum criticality between the Sachdev-Ye-Kitaev liquid and a disordered Fermi liquid

Abstract

We propose a simple solvable variant of the Sachdev-Ye-Kitaev (SYK) model which displays a quantum phase transition from a fast-scrambling non-Fermi liquid to disordered Fermi liquid. Like the canonical SYK model, our variant involves a single species of Majorana fermions connected by all-to-all random four-fermion interactions. The phase transition is driven by a random two-fermion term added to the Hamiltonian whose structure is inspired by proposed solid-state realizations of the SYK model. Analytic expressions for the saddle point solutions at large number N of fermions are obtained and show a characteristic scale-invariant ∼ |ω| −1/2 behavior of the spectral function below the transition which is replaced by a ∼ |ω| −1/3 singularity exactly at the critical point. These results are confirmed by numerical solutions of the saddle point equations and discussed in the broader context of the field.

Rényi entanglement entropy of Fermi and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories

“…in Eq. (53). The addition of a q = 1 quadratic term t i j c † i c j has been shown [30,72] to change the SYK NFL ground state to an interacting zero-dimensional Fermi liquid.…”

“…SYK model [27,28] and its various extensions [30,32,[43][44][45][46][47][48][49] have emerged in recent years as a major paradigm to study phases of strongly interacting fermions, e.g., NFL, marginal and heavy Fermi liquids, strong-coupling superconductivity [32,[46][47][48][49][50][51], and quantum phase transitions [30,48,49,52,53]. Remarkably, these models can be solved exactly in a suitable large-N limit, without resorting to any kind of perturbative treatment.…”

“…The above analysis can also be carried out for the generalizations of the SYK model given in Eqs. (53), (55), and (54). The equations to evaluate the Rényi entropy for the strongly interacting Fermi liquid Hamiltonian in Eq.…”

“…The equations to evaluate the Rényi entropy for the strongly interacting Fermi liquid Hamiltonian in Eq. (53) and BA Hamiltonian in Eq. (54) can be similarly obtained and are given in Appendix E. For extended systems of the kind described by Eq.…”

“…Indeed, we find in literature [73] that the presence of a quadratic term in Eq. (53) drastically reduces the exponentially large density of levels near the ground state, thereby reducing the residual entropy to zero.…”