Phases of quantum dimers from ensembles of classical stochastic trajectories

Abstract

We study the connection between the phase behaviour 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 non-stochastic "tilted" operator that encodes the statistics of time-integrated observables of the classical stochastic problem. This implies a direct relation between the phase behaviour 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 behaviour 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 generalise to other problems.

arXiv comment14 pages, 6 figures

References in corpus (36)

• The large deviation approach to statistical mechanics
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Non equilibrium steady states: fluctuations and large deviations of the density and of the current
• Glassy dynamics of kinetically constrained models
• Dynamics on the Way to Forming Glass: Bubbles in Space-time
• Dynamic first-order phase transition in kinetically constrained models of glasses
• The "Coulomb phase" in frustrated systems
• First-order dynamical phase transition in models of glasses: an approach based on ensembles of histories
• Fluctuations and response of nonequilibrium states
• Thermodynamic formalism for systems with Markov dynamics
• Nonequilibrium Markov processes conditioned on large deviations
• Large deviations and ensembles of trajectories in stochastic models
• Simulating rare events in dynamical processes
• Universal cumulants of the current in diffusive systems on a ring
• Relaxation time for a dimer covering with height representation
• Hyperuniformity and phase separation in biased ensembles of trajectories for diffusive systems
• From quantum mechanics to classical statistical physics: generalized Rokhsar-Kivelson Hamiltonians and the "Stochastic Matrix Form" decomposition
• From classical to quantum dynamics at Rokhsar-Kivelson points
• Population dynamics method with a multi-canonical feedback control
• Classical dimers with aligning interactions on the square lattice
• Finite-temperature critical point of a glass transition
• On bipartite Rokhsar-Kivelson points and Cantor deconfinement
• Exact fluctuations of nonequilibrium steady states from approximate auxiliary dynamics
• Fluctuating hydrodynamics, current fluctuations and hyperuniformity in boundary-driven open quantum chains
• Inactive dynamical phase of a symmetric exclusion process on a ring
• Generic mixed columnar-plaquette phases in Rokhsar-Kivelson models
• The plaquette phase of the square lattice quantum dimer model
• Rare behavior of growth processes via umbrella sampling of trajectories
• Conformal invariance in driven diffusive systems at high currents
• Importance sampling large deviations in nonequilibrium steady states. I
• Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model
• Classical stochastic dynamics and continuous matrix product states: gauge transformations, conditioned and driven processes, and equivalence of trajectory ensembles
• Preserving Correlations Between Trajectories for Efficient Path Sampling
• Critical behavior in the cubic dimer model at nonzero monomer density
• Dynamical dimer correlations at bipartite and non-bipartite Rokhsar-Kivelson points
• Emergence of cooperative dynamics in fully packed classical dimers

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