7 research outputs found
Stochastic series expansion algorithm for the S=1/2 XY model with four-site ring exchange
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.Comment: 23 pages, 21 figure
Loop updates for variational and projector quantum Monte Carlo simulations in the valence-bond basis
We show how efficient loop updates, originally developed for Monte Carlo
simulations of quantum spin systems at finite temperature, can be combined with
a ground-state projector scheme and variational calculations in the valence
bond basis. The methods are formulated in a combined space of spin z-components
and valence bonds. Compared to schemes formulated purely in the valence bond
basis, the computational effort is reduced from up to O(N^2) to O(N) for
variational calculations, where N is the system size, and from O(m^2) to O(m)
for projector simulations, where m>> N is the projection power. These
improvements enable access to ground states of significantly larger lattices
than previously. We demonstrate the efficiency of the approach by calculating
the sublattice magnetization M_s of the two-dimensional Heisenberg model to
high precision, using systems with up to 256*256 spins. Extrapolating the
results to the thermodynamic limit gives M_s=0.30743(1). We also discuss
optimized variational amplitude-product states, which were used as trial states
in the projector simulations, and compare results of projecting different types
of trial states.Comment: 12 pages, 9 figures. v2: Significantly expanded, to appear in Phys.
Rev.
Quantum Monte Carlo simulations of bosonic and fermionic impurities in a two-dimensional hard-core boson system
A two-dimensional lattice hard-core boson system with a small fraction of
bosonic or fermionic impurity particles is studied. The impurities have the
same hopping and interactions as the dominant bosons and their effects are
solely due to quantum statistics. Quantum Monte Carlo simulations are carried
out in which paths of the dominant boson species are sampled and a summation is
performed over all second-species paths compatible with the permutation cycles.
Both kinds of impurities reduce modestly and equally the Kosterliz-Thouless
superfluid transition temperature. However, the effective impurity interactions
are found to be qualitatively different at lower temperatures; fermions are
repulsive and further suppress superfluidity at low temperatures.Comment: 4 pages, 5 figure
Variational quantum Monte Carlo simulations with tensor-network states
We show that the formalism of tensor-network states, such as the matrix
product states (MPS), can be used as a basis for variational quantum Monte
Carlo simulations. Using a stochastic optimization method, we demonstrate the
potential of this approach by explicit MPS calculations for the transverse
Ising chain with up to N=256 spins at criticality, using periodic boundary
conditions and D*D matrices with D up to 48. The computational cost of our
scheme formally scales as ND^3, whereas standard MPS approaches and the related
density matrix renromalization group method scale as ND^5 and ND^6,
respectively, for periodic systems.Comment: 4+ pages, 2 figures. v2: improved data, comparisons with exact
results, to appear in Phys Rev Let