44 research outputs found
Random walks near Rokhsar-Kivelson points
There is a class of quantum Hamiltonians known as
Rokhsar-Kivelson(RK)-Hamiltonians for which static ground state properties can
be obtained by evaluating thermal expectation values for classical models. The
ground state of an RK-Hamiltonian is known explicitly, and its dynamical
properties can be obtained by performing a classical Monte Carlo simulation. We
discuss the details of a Diffusion Monte Carlo method that is a good tool for
studying statics and dynamics of perturbed RK-Hamiltonians without time
discretization errors. As a general result we point out that the relation
between the quantum dynamics and classical Monte Carlo simulations for
RK-Hamiltonians follows from the known fact that the imaginary-time evolution
operator that describes optimal importance sampling, in which the exact ground
state is used as guiding function, is Markovian. Thus quantum dynamics can be
studied by a classical Monte Carlo simulation for any Hamiltonian that is free
of the sign problem provided its ground state is known explicitly.Comment: 12 pages, 9 figures, RevTe
Quantum renormalization of high energy excitations in the 2D Heisenberg antiferromagnet
We find using Monte Carlo simulations of the spin-1/2 2D square lattice
nearest neighbour quantum Heisenberg antiferromagnet that the high energy peak
locations at (pi,0) and (pi/2,pi/2) differ by about 6%, (pi/2,pi/2) being the
highest. This is a deviation from linear spin wave theory which predicts equal
magnon energies at these points.Comment: Final version, Latex using iopart & epsfi
Quantum Phase Transitions in Coupled Dimer Compounds
We study the critical properties in cubic systems of antiferromagnetically
coupled spin dimers near magnetic-field induced quantum phase transitions. The
quantum critical points in the zero-temperature phase diagrams are determined
from quantum Monte Carlo simulations. Furthermore, scaling properties of the
uniform magnetization and the staggered transverse magnetization across the
quantum phase transition in magnetic fields are calculated. The critical
exponents are derived from Ginzburg-Landau theory. We find excellent agreement
between the quantum Monte Carlo simulations and the analytical results.Comment: 7 pages, 9 eps-figure
Antiferromagnetic noise correlations in optical lattices
We analyze how noise correlations probed by time-of-flight (TOF) experiments
reveal antiferromagnetic (AF) correlations of fermionic atoms in
two-dimensional (2D) and three-dimensional (3D) optical lattices. Combining
analytical and quantum Monte Carlo (QMC) calculations using experimentally
realistic parameters, we show that AF correlations can be detected for
temperatures above and below the critical temperature for AF ordering. It is
demonstrated that spin-resolved noise correlations yield important information
about the spin ordering. Finally, we show how to extract the spin correlation
length and the related critical exponent of the AF transition from the noise.Comment: 4 pages, 4 figure
Sublattice ordering in a dilute ensemble of defects in graphene
Defects in graphene, such as vacancies or adsorbents attaching themselves to
carbons, may preferentially take positions on one of its two sublattices, thus
breaking the global lattice symmetry. This leads to opening a gap in the
electronic spectrum. We show that such a sublattice ordering may spontaneously
occur in a dilute ensemble defects, due to the long-range interaction between
them mediated by electrons. As a result sublattice-ordered domains may form,
with electronic properties characteristic of a two-dimensional topological
insulator.Comment: to appear in Europhysics Letter
One-dimensional phase transitions in a two-dimensional optical lattice
A phase transition for bosonic atoms in a two-dimensional anisotropic optical
lattice is considered. If the tunnelling rates in two directions are different,
the system can undergo a transition between a two-dimensional superfluid and a
one-dimensional Mott insulating array of strongly coupled tubes. The connection
to other lattice models is exploited in order to better understand the phase
transition. Critical properties are obtained using quantum Monte Carlo
calculations. These critical properties are related to correlation properties
of the bosons and a criterion for commensurate filling is established.Comment: 14 pages, 8 figure
Measuring spin correlations in optical lattices using superlattice potentials
We suggest two experimental methods for probing both short- and long-range
spin correlations of atoms in optical lattices using superlattice potentials.
The first method involves an adiabatic doubling of the periodicity of the
underlying lattice to probe neighboring singlet (triplet) correlations for
fermions (bosons) by the occupation of the new vibrational ground state. The
second method utilizes a time-dependent superlattice potential to generate
spin-dependent transport by any number of prescribed lattice sites, and probes
correlations by the resulting number of doubly occupied sites. For
experimentally relevant parameters, we demonstrate how both methods yield large
signatures of antiferromagnetic (AF) correlations of strongly repulsive
fermionic atoms in a single shot of the experiment. Lastly, we show how this
method may also be applied to probe d-wave pairing, a possible ground state
candidate for the doped repulsive Hubbard model.Comment: 5 pages, 3 figure
Transition matrix Monte Carlo method for quantum systems
We propose an efficient method for Monte Carlo simulation of quantum lattice
models. Unlike most other quantum Monte Carlo methods, a single run of the
proposed method yields the free energy and the entropy with high precision for
the whole range of temperature. The method is based on several recent findings
in Monte Carlo techniques, such as the loop algorithm and the transition matrix
Monte Carlo method. In particular, we derive an exact relation between the DOS
and the expectation value of the transition probability for quantum systems,
which turns out to be useful in reducing the statistical errors in various
estimates.Comment: 6 pages, 4 figure
Bosons in optical lattices - from the Mott transition to the Tonks-Girardeau gas
We present results from quantum Monte Carlo simulations of trapped bosons in
optical lattices, focusing on the crossover from a gas of softcore bosons to a
Tonks-Girardeau gas in a one-dimensional optical lattice. We find that
depending on the quantity being measured, the behavior found in the
Tonks-Girardeau regime is observed already at relatively small values of the
interaction strength. A finite critical value for entering the Tonks-Girardeau
regime does not exist. Furthermore, we discuss the computational efficiency of
two quantum Monte Carlo methods to simulate large scale trapped bosonic
systems: directed loops in stochastic series expansions and the worm algorithm.Comment: 7 pages with 9 figures;v2: improved discussion on Tonks-Girardeau ga
Intermediate temperature dynamics of one-dimensional Heisenberg antiferromagnets
We present a general theory for the intermediate temperature (T) properties
of Heisenberg antiferromagnets of spin-S ions on p-leg ladders, valid for 2Sp
even or odd. Following an earlier proposal for 2Sp even (Damle and Sachdev,
cond-mat/9711014), we argue that an integrable, classical, continuum model of a
fixed-length, 3-vector applies over an intermediate temperature range; this
range becomes very wide for moderate and large values of 2Sp. The coupling
constants of the effective model are known exactly in terms of the energy gap
above the ground state (for 2Sp even) or a crossover scale (for 2Sp odd).
Analytic and numeric results for dynamic and transport properties are obtained,
including some exact results for the spin-wave damping. Numerous quantitative
predictions for neutron scattering and NMR experiments are made. A general
discussion on the nature of T>0 transport in integrable systems is also
presented: an exact solution of a toy model proves that diffusion can exist in
integrable systems, provided proper care is taken in approaching the
thermodynamic limit.Comment: 38 pages, including 12 figure