A model for continuous thermal Metal to Insulator Transition

TL;DR

This work constructs a disordered chain of interacting Majorana fermions built from coupled SYK clusters to realize a metal-insulator transition in a controlled large-$N$ setting. By analyzing saddle-point equations and performing a large-$q$ expansion, the authors show that tuning an onsite interaction $u$ drives a transition from a diffusive thermal metal with finite entropy density to an insulator with zero entropy density, accompanied by spontaneous time-reversal symmetry breaking. In the metallic phase, transport is governed by inter-cluster SYK interactions and yields a finite diffusion constant, while infrared analysis indicates diffusion vanishes in the insulating phase; an effective quasi-Goldstone action explains the scaling that suppresses energy diffusion. The results illuminate ETH-MBL-like transitions in interacting, disordered Majorana systems and demonstrate how symmetry breaking controls transport in this analytically tractable setting.

Abstract

We propose a $d-$dimensional interacting Majorana fermion model with quenched disorder, which gives us a continuous quantum phase transition between a diffusive thermal metal phase with a finite entropy density to an insulator phase with zero entropy density. This model is based on coupled Sachdev-Ye-Kitaev model clusters, and hence has a controlled large-$N$ limit. The metal-insulator transition is accompanied by a spontaneous time-reversal symmetry breaking. We perform controlled calculations to show that the diffusion constant jumps to zero discontinuously at the metal-insulator transition, while the time-reversal symmetry breaking order parameter increases continuously.

Figures (1)

• Figure 1: The schematic structure of our model Eq. \ref{['chain']}.