Quantum mechanical and information theoretic view on classical glass transitions

Abstract

Using the mapping of the Fokker-Planck description of classical stochastic dynamics onto a quantum Hamiltonian, we argue that a dynamical glass transition in the former must have a precise definition in terms of a quantum phase transition in the latter. At the dynamical level, the transition corresponds to a collapse of the excitation spectrum at a critical point. At the static level, the transition affects the ground state wavefunction: while in some cases it could be picked up by the expectation value of a local operator, in others the order may be non-local, and impossible to be determined with any local probe. Here we propose instead to use concepts from quantum information theory that are not centered around local order parameters, such as fidelity and entanglement measures. We show that for systems derived from the mapping of classical stochastic dynamics, singularities in the fidelity susceptibility translate directly into singularities in the heat capacity of the classical system. In classical glassy systems with an extensive number of metastable states, we find that the prefactor of the area law term in the entanglement entropy jumps across the transition. We also discuss how entanglement measures can be used to detect a growing correlation length that diverges at the transition. Finally, we illustrate how static order can be hidden in systems with a macroscopically large number of degenerate equilibrium states by constructing a three dimensional lattice gauge model with only short-range interactions but with a finite temperature continuous phase transition into a massively degenerate phase.

13 pages + appendix (9 pages), 8 figures (new version: small corrections during publication)

References in corpus (19)

• Criticality, the area law, and the computational power of PEPS
• Fidelity, dynamic structure factor, and susceptibility in critical phenomena
• Dynamic first-order phase transition in kinetically constrained models of glasses
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Topological Order and Conformal Quantum Critical Points
• Bipartite entanglement and entropic boundary law in lattice spin systems
• Ground state entanglement and geometric entropy in the Kitaev's model
• Rigorous Inequalities between Length and Time Scales in Glassy Systems
• Topological order in a 3D toric code at finite temperature
• Quantum phase transitions and quantum fidelity in free fermion graphs
• A quantum topological phase transition at the microscopic level
• Fidelity analysis of topological quantum phase transitions
• Space-time thermodynamics and subsystem observables in a kinetically constrained model of glassy systems
• Quantum criticality, lines of fixed points, and phase separation in doped two-dimensional quantum dimer models
• Fidelity approach to the disordered quantum XY model
• Scaling of the fidelity susceptibility in a disordered quantum spin chain
• Zero-temperature Kosterlitz-Thouless transition in a two-dimensional quantum system
• Doping quantum dimer models on the square lattice
• Glassy behaviour in an exactly solved spin system with a ferromagnetic transition

Cited by in corpus (1)

• Finite-temperature critical point of a glass transition