# Instability of the non-Fermi liquid state of the Sachdev-Ye-Kitaev Model

## TL;DR

This paper investigates how perturbations affect the chaotic non-Fermi liquid phase of the SYK model, revealing phase transitions and new fixed points related to symmetry breaking and conformal field theories.

## Contribution

It demonstrates the instability of the SYK non-Fermi liquid phase under certain four-fermion perturbations and identifies resulting phase transitions and fixed points.

## Key findings

- Perturbations can be marginally relevant or irrelevant depending on their sign.
- Changing the sign of perturbations induces a quantum phase transition with time-reversal symmetry breaking.
- New conformal field theory fixed points emerge from these perturbations.

## Abstract

We study a series of perturbations on the Sachdev-Ye-Kitaev (SYK) model. We show that the chaotic non-Fermi liquid phase described by the ordinary $q = 4$ SYK model has marginally relevant/irrelevant (depending on the sign of the coupling constants) four-fermion perturbations allowed by symmetry. Changing the sign of one of these four-fermion perturbations leads to a continuous chaotic-nonchaotic quantum phase transition of the system accompanied by a spontaneous time-reversal symmetry breaking. Starting with the SYK$_q$ model with a $q-$fermion interaction, similar perturbations can lead to a series of new interacting conformal field theory fixed points.