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

## TL;DR

This paper introduces a solvable model that exhibits a quantum phase transition from a non-Fermi liquid to a disordered Fermi liquid, providing analytical and numerical insights into quantum criticality in SYK-like systems.

## Contribution

A new solvable variant of the SYK model with a quantum phase transition driven by a two-fermion term, including analytical solutions and spectral function analysis.

## Key findings

- Spectral function scales as ||^{-1/2} below the transition
- At the critical point, spectral function exhibits ||^{-1/3} singularity
- Analytical saddle point solutions match numerical results

## 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 $\sim |\omega|^{-1/2}$ behavior of the spectral function below the transition which is replaced by a $\sim |\omega|^{-1/3}$ 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.