Directed Loop Updates for Quantum Lattice Models

Abstract

This article outlines how the quantum Monte Carlo directed loop update recently introduced can be applied to a wide class of quantum lattice models. Several models are considered: Spin-S XXZ models with longitudinal and transverse magnetic fields, boson models with two-body interactions, and 1D spinful fermion models. Expressions are given for the parameter regimes were very efficient "no-bounce" quantum Monte Carlo algorithms can be found.

18 pages, 19 figures

Cited by in corpus (64)

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• Quantum Monte Carlo simulations of confined bosonic atoms in optical lattices
• Entanglement and Spontaneous Symmetry Breaking in Quantum Spin Models
• Superfluid-insulator transitions of two-species Bosons in an optical lattice
• Bosons in one-dimensional incommensurate superlattices
• The ground state entanglement in the $XXZ$ model
• Quenching the Haldane gap in spin-1 Heisenberg antiferromagnets
• Engineering Local optimality in Quantum Monte Carlo algorithms
• Directed-loop Monte Carlo simulations of vertex models
• Momentum distribution of 1D Bose gases at the quasi-condensation crossover: theoretical and experimental investigation
• Momentum-space correlations of a one-dimensional Bose gas
• Higher-form symmetry breaking at Ising transitions
• Loop updates for quantum Monte Carlo simulations in the canonical ensemble
• Universal Scaling of the Conductivity at the Superfluid-Insulator Phase Transition
• Characterizing the Haldane phase in quasi-one-dimensional spin-1 Heisenberg antiferromagnets
• Single-particle versus pair condensation of hard-core bosons with correlated hopping
• Mott glass in site-diluted S=1 antiferromagnets with single-ion anisotropy
• Comparison of S=0 and S=1/2 Impurities in Haldane Chain Compound, $Y_{2}BaNi{O}_5$
• Directed geometrical worm algorithm applied to the quantum rotor model
• Optimal Monte Carlo Updating
• Quantum Monte Carlo simulation in the canonical ensemble at finite temperature
• Ultracold atoms in one-dimensional optical lattices approaching the Tonks-Girardeau regime
• Quantum phase transitions of interacting bosons on hyperbolic lattices
• Stochastic series expansion algorithm for the S=1/2 XY model with four-site ring exchange
• Concurrence in the two dimensional XXZ- and transverse field Ising-models
• Crossover effects in the random exchange spin-1/2 antiferromagnetic chain
• Magnetism in a family of $S=1$ square lattice antiferromagnets Ni$X_2$(pyz)${}_2$ ($X=$ Cl, Br, I, NCS; pyz = pyrazine)
• Construction of localized wave functions for a disordered optical lattice and analysis of the resulting Hubbard model parameters
• Quantum Monte Carlo simulations in the trimer basis: first-order transitions and thermal critical points in frustrated trilayer magnets
• Height-conserving quantum dimer models
• Probing correlated phases of bosons in optical lattices via trap squeezing
• Cluster algorithms for frustrated two dimensional Ising antiferromagnets via dual worm constructions
• Spin vs. bond correlations along dangling edges of quantum critical magnets
• Length-Dependent Conductance of a Spin-Incoherent Hubbard chain; Monte Carlo Calculations
• Statistical mechanics of dimers on quasiperiodic Ammann-Beenker tilings
• Anomalous quantum glass of bosons in a random potential in two dimensions
• Magnon Landau levels in the strained antiferromagnetic honeycomb nanoribbons
• DSQSS: Discrete Space Quantum Systems Solver
• Quantum Monte Carlo study of honeycomb antiferromagnets under a triaxial strain
• Pairing, crystallization and string correlations of mass-imbalanced atomic mixtures in one-dimensional optical lattices
• Exploring the grand-canonical phase diagram of interacting bosons in optical lattices by trap squeezing
• Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar-Bernevig-Hughes model
• Unconventional ferromagnetism and spin-triplet superconductivity in the imbalanced Kagome-lattice Hubbard model
• A Rényi entropy perspective on topological order in classical toric code models
• Magnons in a two dimensional transverse field XXZ model
• Hubbard and Heisenberg models on hyperbolic lattices: Metal-insulator transitions, global antiferromagnetism, and enhanced boundary fluctuations
• Study of long-range orders of hard-core bosons coupled to cooperative normal modes in two-dimensional lattices
• Study of supersolidity in the two-dimensional Hubbard-Holstein model
• Weak topological insulating phases of hard-core-bosons on the honeycomb lattice
• Spin-Hall magnetoresistance in quasi-two-dimensional antiferromagnetic insulator/metal bilayer systems
• One-dimensional phase transitions in a two-dimensional optical lattice
• Quantum Monte Carlo simulations of highly frustrated magnets in a cluster basis: The two-dimensional Shastry-Sutherland model
• High-field spin-flop state in green dioptase
• Measuring Non-local Brane Order with Error-corrected Parity Snapshots
• Hardcore bosonic domain walls on honeycomb lattice
• Addressing general measurements in quantum Monte Carlo
• Mixed-order transition and tricritical point associated with checkerboard supersolidity in the two-dimensional $t_2-V_1$ model
• Loop Algorithm for Quantum Transverse Ising Model in a Longitudinal Field
• Coexistence of long-range orders in a Bose-Holstein model
• Minimal energy ensemble Monte Carlo for the partition function of fermions coupled to classical fields
• Phase transitions and crtical exponents in the six-vertex model on kagome lattices
• Bell sampling in Quantum Monte Carlo simulations
• Double Supersolid Phase in a Bosonic t-J-V Model with Rydberg Atoms
• Coupled dimerized alternating-bond quantum spin chains in the distorted honeycomb-lattice magnet Cu${}_5$SbO${}_6$