Stochastic series expansion algorithm for the S=1/2 XY model with four-site ring exchange

Abstract

We describe a stochastic series expansion (SSE) quantum Monte Carlo method for a two-dimensional S=1/2 XY-model (or, equivalently, hard-core bosons at half-filling) which in addition to the standard pair interaction J includes a four-particle term K that flips spins on a square plaquette. The model has three ordered ground state phases; for K/J<8 it has long-range xy spin order (superfluid bosons), for K/J>15 it has staggered spin order in the z direction (charge-density-wave), and between these phases it is in a state with columnar order in the bond and plaquette energy densities. We discuss an implementation of directed-loop updates for the SSE simulations of this model and also introduce a "multi-branch" cluster update which significantly reduces the autocorrelation times for large K/J. In addition to the pure J-K model, which in the z basis has only off-diagonal terms, we also discuss modifications of the algorithm needed when various diagonal interactions are included.

23 pages, 21 figures

References in corpus (14)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Generalized Directed Loop Method for Quantum Monte Carlo Simulations
• Stochastic series expansion method for quantum Ising models with arbitrary interactions
• Putting competing orders in their place near the Mott transition
• Recent Developments of World-Line Monte Carlo Methods
• Quantum Monte Carlo study of S=1/2 weakly-anisotropic antiferromagnets on the square lattice
• Cyclic exchange, isolated states and spinon deconfinement in an XXZ Heisenberg model on the checkerboard lattice
• Two-Dimensional Quantum XY Model with Ring Exchange and External Field
• Numerical study of fractionalization in an Easy-axis Kagome antiferromagnet
• Optimal Monte Carlo Updating
• Persistent superfluid phase in a three-dimensional quantum XY model with ring exchange

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• Sweeping cluster algorithm for quantum spin systems with strong geometric restrictions
• Hilbert space fragmentation in a 2D quantum spin system with subsystem symmetries
• Single-particle versus pair condensation of hard-core bosons with correlated hopping
• Building models of topological quantum criticality from pivot Hamiltonians
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• Magnetic three states of matter: A quantum Monte Carlo study of spin liquids
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• Introduction to the variational and diffusion Monte Carlo methods
• Off-site trimer superfluid on a one-dimensional optical lattice
• Spin dynamics of the planar kagome lattice ferromagnet with four-site ring exchange processes
• Quantum orders in the frustrated Ising model on the bathroom tile lattice
• Bell sampling in Quantum Monte Carlo simulations
• Breathing kagome XY quantum magnet with four-site ring exchange