Phases of quantum dimers from ensembles of classical stochastic trajectories

Tom Oakes, Stephen Powell, Claudio Castelnovo, Austen Lamacraft, and Juan P. Garrahan
Phys. Rev. B 98, 064302 – Published 8 August 2018

Abstract

We study the connection between the phase behavior of quantum dimers and the dynamics of classical stochastic dimers. At the so-called Rokhsar-Kivelson (RK) point a quantum dimer Hamiltonian is equivalent to the Markov generator of the dynamics of classical dimers. A less well understood fact is that away from the RK point the quantum-classical connection persists: in this case the Hamiltonian corresponds to a nonstochastic “tilted” operator that encodes the statistics of time-integrated observables of the classical stochastic problem. This implies a direct relation between the phase behavior of quantum dimers and properties of ensembles of stochastic trajectories of classical dimers. We make these ideas concrete by studying fully packed dimers on the square lattice. Using transition path sampling—supplemented by trajectory umbrella sampling—we obtain the large deviation statistics of dynamical activity in the classical problem, and show the correspondence between the phase behavior of the classical and quantum systems. The transition at the RK point between quantum phases of distinct order corresponds, in the classical case, to a trajectory phase transition between active and inactive dynamical phases. Furthermore, from the structure of stochastic trajectories in the active dynamical phase we infer that the ground state of quantum dimers has columnar order to one side of the RK point. We discuss how these results relate to those from quantum Monte Carlo, and how our approach may generalize to other problems.

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  • Received 22 March 2018
  • Revised 10 July 2018

DOI:https://doi.org/10.1103/PhysRevB.98.064302

©2018 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Tom Oakes1,*, Stephen Powell1, Claudio Castelnovo2, Austen Lamacraft2, and Juan P. Garrahan1

  • 1School of Physics and Astronomy and Centre for the Mathematics and Theoretical Physics of Quantum Non-Equilibrium Systems, University of Nottingham, Nottingham NG7 2RD, United Kingdom
  • 2TCM Group, Cavendish Laboratory, University of Cambridge, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom

  • *tom.oakes@nottingham.ac.uk

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Issue

Vol. 98, Iss. 6 — 1 August 2018

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