Quantum criticality of granular SYK matter

TL;DR

A zero-temperature quantum phase transition between an insulating phase at weak and a metallic phase at strong hopping is identified within the framework of Schwarzian field theory.

Abstract

We consider granular quantum matter defined by Sachdev-Ye-Kitaev (SYK) dots coupled via random one-body hopping. Within the framework of Schwarzian field theory, we identify a zero temperature quantum phase transition between an insulating phase at weak and a metallic phase at strong hopping. The critical hopping strength scales inversely with the number of degrees of freedom on the dots. The increase of temperature out of either phase induces a crossover into a regime of strange metallic behavior.

Figures (4)

• Figure 1: Phase diagram of SYK array: $T$ vs. dimensionless hopping strength $\lambda=(NV/J)^2$. At a critical value, $\lambda_c=8/Z$, the system undergoes a zero temperature metal--insulator QPT. The two lines $T_\mathrm{I}(\lambda)$ and $T_\mathrm{FL}(\lambda)$ mark insulator (I) to strange metal (SM) and FL to SM crossovers, correspondingly. The insets shows thermal resistivity $T/\kappa(T)$ vs. $T$ for $\lambda<\lambda_c$, $\lambda=\lambda_c$ and $\lambda>N>\lambda_c$.
• Figure 2: RG flow in the plane of couplings $(\lambda=mw,m)$; here $\lambda_c=8/Z$ and $m_c={\cal O}(1)/J$. The initial values are $m(0)=N/J$ and $\lambda(0)=(NV/J)^2$.
• Figure 3: The log-linear plot of the effective scaling dimension of fermion operators $\Delta_\psi$, as a function of the running scale $m$ measured in units of the interaction strength $J$. For its exact definition in terms of the two-point function of the Schwarzian theory, we refer to the Supplemental Material.
• Figure 4: The log-log plot of the fast Green's functions $G_{f}(s)$ versus time $s$ used in the RG analysis.