The Hilbert-glass transition: new universality of temperature-tuned many-body dynamical quantum criticality

TL;DR

This paper introduces a real-space renormalization group method for excited states to analyze a new class of temperature-tuned dynamical quantum criticality, exemplified by a 1D disordered transverse field Ising model.

Contribution

It develops RSRG-X, a novel technique for studying finite-temperature dynamical phase transitions in many-body localized systems.

Findings

Identifies a finite-temperature transition between localized phases.

Characterizes non-analyticities in dynamic spin correlations.

Finds vanishing heat conductivity at the transition.

Abstract

We consider a new class of unconventional critical phenomena that is characterized by singularities only in dynamical quantities and has no thermodynamic signatures. A possible example is the recently proposed many-body localization transition, in which transport coefficients vanish at a critical temperature. Describing this unconventional quantum criticality has been technically challenging as understanding the finite-temperature dynamics requires the knowledge of a large number of many-body eigenstates. Here we develop a real-space renormalization group method for excited state (RSRG-X), that allow us to overcome this challenge, and establish the existence and universal properties of such temperature-tuned dynamical phase transitions. We characterize a specific example: the 1D disordered transverse field Ising model with interactions. Using RSRG-X, we find a finite-temperature transition, between two localized phases, characterized by non-analyticities of the dynamic spin correlation function and the low frequency heat conductivity.