Quantum criticality and duality in the SYK/AdS$_2$ chain

TL;DR

This paper establishes a holographic duality between the quantum critical point in the SYK chain and a gravitational description involving AdS$_2$ chains, revealing universal features of phase transitions in such systems.

Contribution

It demonstrates an exact correspondence between the SYK chain's quantum criticality and a double-trace deformation in an AdS$_2$ chain, providing new insights into holographic dualities.

Findings

Exact reproduction of susceptibility and RG equations in holographic model

Infrared geometry of the SYK chain's diffusive metal is AdS$_2$

Universal features of double-trace deformations in black holes with AdS$_2$ horizons

Abstract

We show that the quantum critical point (QCP) between a diffusive metal and ferromagnetic (or antiferromagnetic) phases in the SYK chain has a gravitational description corresponding to the double-trace deformation in an AdS$_2$ chain. Specifically, by studying a double-trace deformation of a $Z_2$ scalar in an AdS$_2$ chain where the $Z_2$ scalar is dual to the order parameter in the SYK chain, we find that the susceptibility and renormalization group equation describing the QCP in the SYK chain can be exactly reproduced in the holographic model. Our results suggest that the infrared geometry in the gravity theory dual to the diffusive metal of the SYK chain is also an AdS$_2$ chain. We further show that the transition in SYK model captures universal information about double-trace deformation in generic black holes with near horizon AdS$_2$ spacetime.