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.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.

arXiv:1802.09576Physical review. B./Physical review. BAug 8, 201826 citations

Phase Transitions and Lattice Systems

Sergio Cecotti

UNITEXT for physicsJan 1, 20240 citations

Quantum liquid of repulsively bound pairs of particles in a lattice

David Petrosyan, Bernd G Schmidt, J. R. Anglin +1 more

Repulsively interacting particles in a periodic potential can form bound composite objects, whose dissociation is suppressed by a band gap. Nearly pure samples of such repulsively bound pairs of cold atoms---``dimers''---have recently been prepared by Winkler et al. [Nature (London) 441, 853 (2006)]. We here derive an effective Hamiltonian for a lattice loaded with dimers only and discuss its implications for the many-body dynamics of the system. We find that the dimer-dimer interaction includes strong on-site repulsion and nearest-neighbor attraction which always dominates over the dimer kinetic energy at low temperatures. The dimers then form incompressible, minimal-surface ``droplets'' of a quantum lattice liquid. For low lattice filling, the effective Hamiltonian can be mapped onto the spin- $1∕2$ $XXZ$ model with fixed total magnetization which exhibits a first-order phase transition from the droplet to a gas phase. This opens the door to studying first-order phase transitions using highly controllable ultracold atoms.Repulsively interacting particles in a periodic potential can form bound composite objects, whose dissociation is suppressed by a band gap. Nearly pure samples of such repulsively bound pairs of cold atoms---``dimers''---have recently been prepared by Winkler et al. [Nature (London) 441, 853 (2006)]. We here derive an effective Hamiltonian for a lattice loaded with dimers only and discuss its implications for the many-body dynamics of the system. We find that the dimer-dimer interaction includes strong on-site repulsion and nearest-neighbor attraction which always dominates over the dimer kinetic energy at low temperatures. The dimers then form incompressible, minimal-surface ``droplets'' of a quantum lattice liquid. For low lattice filling, the effective Hamiltonian can be mapped onto the spin-$1∕2$ $XXZ$ model with fixed total magnetization which exhibits a first-order phase transition from the droplet to a gas phase. This opens the door to studying first-order phase transitions using highly controllable ultracold atoms.

arXiv:cond-mat/0610198Physical Review ASep 12, 200790 citations

1∕2

XXZ

model with fixed total magnetization which exhibits a first-order phase transition from the droplet to a gas phase. This opens the door to studying first-order phase transitions using highly controllable ultracold atoms.