Skip to main content
Article thumbnail
Location of Repository

Quantum mechanical and information theoretic view on classical glass transitions

By Claudio Castelnovo, Claudio Chamon and David Sherrington

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 wave function: while in some cases it could be picked up by the expectation value of a local operator, in others the order may be nonlocal and impossible to be determined with any local probe. Here we instead propose 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

Topics: ISING SPIN-GLASS, GRIFFITHS SINGULARITIES, PHASE-TRANSITIONS, GONIHEDRIC ACTION, STOCHASTIC-MODEL, TRANSFER-MATRIX, SYSTEMS, DYNAMICS, BEHAVIOR, ORDER, Faculty of Science\Physics, Research Groups and Centres\Physics\Low Temperature Physics
Year: 2010
DOI identifier: 10.1103/PhysRevB.81.184303
OAI identifier: oai:repository.royalholloway.ac.uk:d2a4de3c-633a-5e9f-1d30-afbfb48110da/7
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
  • http://dx.doi.org/10.1103/Phys... (external link)
  • https://repository.royalhollow... (external link)
  • http://prb.aps.org/abstract/PR... (external link)
  • Suggested articles


    To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.