Finite-temperature critical point of a glass transition

TL;DR

This paper introduces a softened kinetically constrained model of glass-forming liquids that exhibits a finite-temperature dynamical critical point, linking classical glass transitions to quantum phase transitions.

Contribution

It extends the simplest kinetically constrained model by allowing constraint violations, revealing a finite-temperature critical point and establishing connections to quantum phase transitions.

Findings

Supports a first-order dynamical phase transition

Identifies a finite-temperature dynamical critical point

Maps dynamical phase transitions to quantum and classical thermodynamic transitions

Abstract

We generalize the simplest kinetically constrained model of a glass-forming liquid by softening kinetic constraints, allowing them to be violated with a small finite rate. We demonstrate that this model supports a first-order dynamical (space-time) phase transition, similar to those observed with hard constraints. In addition, we find that the first-order phase boundary in this softened model ends in a finite-temperature dynamical critical point, which we expect to be present in natural systems. We discuss links between this critical point and quantum phase transitions, showing that dynamical phase transitions in $d$ dimensions map to quantum transitions in the same dimension, and hence to classical thermodynamic phase transitions in $d+1$ dimensions. We make these links explicit through exact mappings between master operators, transfer matrices, and Hamiltonians for quantum spin chains.