Quantum discontinuity fixed point and renormalization group flow of the SYK model

TL;DR

This paper analyzes the RG flow of the SYK model, revealing fixed points and quantum criticality at a first-order transition, challenging classical transition descriptions and suggesting quantum phase coexistence as a critical state.

Contribution

It identifies fixed points and quantum critical behavior in the SYK model's RG flow, highlighting a novel quantum first-order transition with persistent criticality.

Findings

Stable non-Fermi liquid fixed point confirmed

Discontinuity fixed point with quantum critical spectrum identified

Quantum phase coexistence as a genuine critical state

Abstract

We determine the global renormalization group (RG) flow of the Sachdev-Ye-Kitaev (SYK) model. This flow allows for an understanding of the surprising role of critical slowing down at a quantum first-order transition in strongly-correlated electronic systems. From a simple truncation of the infinite hierarchy of the exact functional RG flow equations we identify several fixed points: Apart from a stable fixed point, associated with the celebrated non-Fermi liquid state of the model, we find another stable fixed point related to an integer-valence state. These stable fixed points are separated by a discontinuity fixed point with one relevant direction, describing a quantum first-order transition. Most notably, the fermionic spectrum continues to be quantum critical even at the discontinuity fixed point. This rules out a description of this quantum first-order transition in terms of a local effective Ising variable that is established for classical transitions. It reveals that quantum phase coexistence can be a genuine critical state of matter.