479 research outputs found
Non-local updates for quantum Monte Carlo simulations
We review the development of update schemes for quantum lattice models
simulated using world line quantum Monte Carlo algorithms. Starting from the
Suzuki-Trotter mapping we discuss limitations of local update algorithms and
highlight the main developments beyond Metropolis-style local updates: the
development of cluster algorithms, their generalization to continuous time, the
worm and directed-loop algorithms and finally a generalization of the flat
histogram method of Wang and Landau to quantum systems.Comment: 14 pages, article for the proceedings of the "The Monte Carlo Method
in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis
Algorithm", Los Alamos, June 9-11, 200
Relevance of the Heisenberg-Kitaev model for the honeycomb lattice iridates A_2IrO_3
Combining thermodynamic measurements with theoretical density functional and
thermodynamic calculations we demonstrate that the honeycomb lattice iridates
A2IrO3 (A = Na, Li) are magnetically ordered Mott insulators where the
magnetism of the effective spin-orbital S = 1/2 moments can be captured by a
Heisenberg-Kitaev (HK) model with Heisenberg interactions beyond
nearest-neighbor exchange. Experimentally, we observe an increase of the
Curie-Weiss temperature from \theta = -125 K for Na2IrO3 to \theta = -33 K for
Li2IrO3, while the antiferromagnetic ordering temperature remains roughly the
same T_N = 15 K for both materials. Using finite-temperature functional
renormalization group calculations we show that this evolution of \theta, T_N,
the frustration parameter f = \theta/T_N, and the zig-zag magnetic ordering
structure suggested for both materials by density functional theory can be
captured within this extended HK model. Combining our experimental and
theoretical results, we estimate that Na2IrO3 is deep in the magnetically
ordered regime of the HK model (\alpha \approx 0.25), while Li2IrO3 appears to
be close to a spin-liquid regime (0.6 < \alpha < 0.7).Comment: Version accepted for publication in PRL. Additional DFT and
thermodynamic calculations have been included. 6 pages of supplementary
material include
Ramping fermions in optical lattices across a Feshbach resonance
We study the properties of ultracold Fermi gases in a three-dimensional
optical lattice when crossing a Feshbach resonance. By using a zero-temperature
formalism, we show that three-body processes are enhanced in a lattice system
in comparison to the continuum case. This poses one possible explanation for
the short molecule lifetimes found when decreasing the magnetic field across a
Feshbach resonance. Effects of finite temperatures on the molecule formation
rates are also discussed by computing the fraction of double-occupied sites.
Our results show that current experiments are performed at temperatures
considerably higher than expected: lower temperatures are required for
fermionic systems to be used to simulate quantum Hamiltonians. In addition, by
relating the double occupancy of the lattice to the temperature, we provide a
means for thermometry in fermionic lattice systems, previously not accessible
experimentally. The effects of ramping a filled lowest band across a Feshbach
resonance when increasing the magnetic field are also discussed: fermions are
lifted into higher bands due to entanglement of Bloch states, in good agreement
with recent experiments.Comment: 9 pages, 7 figure
Overcoming the critical slowing down of flat-histogram Monte Carlo simulations: Cluster updates and optimized broad-histogram ensembles
We study the performance of Monte Carlo simulations that sample a broad
histogram in energy by determining the mean first-passage time to span the
entire energy space of d-dimensional ferromagnetic Ising/Potts models. We first
show that flat-histogram Monte Carlo methods with single-spin flip updates such
as the Wang-Landau algorithm or the multicanonical method perform sub-optimally
in comparison to an unbiased Markovian random walk in energy space. For the
d=1,2,3 Ising model, the mean first-passage time \tau scales with the number of
spins N=L^d as \tau \propto N^2L^z. The critical exponent z is found to
decrease as the dimensionality d is increased. In the mean-field limit of
infinite dimensions we find that z vanishes up to logarithmic corrections. We
then demonstrate how the slowdown characterized by z>0 for finite d can be
overcome by two complementary approaches - cluster dynamics in connection with
Wang-Landau sampling and the recently developed ensemble optimization
technique. Both approaches are found to improve the random walk in energy space
so that \tau \propto N^2 up to logarithmic corrections for the d=1 and d=2
Ising model
Optimized Folding Simulations of Protein A
We describe optimized parallel tempering simulations of the 46-residue
B-fragment of protein A. Native-like configurations with a root-mean-square
deviation of approximately 3A to the experimentally determined structure
(Protein Data Bank identifier 1BDD) are found. However, at biologically
relevant temperatures such conformations appear with only about 10% frequency
in our simulations. Possible short comings in our energy function are
discussed.Comment: 6 pages, 8 figure
Generalized Ensemble and Tempering Simulations: A Unified View
From the underlying Master equations we derive one-dimensional stochastic
processes that describe generalized ensemble simulations as well as tempering
(simulated and parallel) simulations. The representations obtained are either
in the form of a one-dimensional Fokker-Planck equation or a hopping process on
a one-dimensional chain. In particular, we discuss the conditions under which
these representations are valid approximate Markovian descriptions of the
random walk in order parameter or control parameter space. They allow a unified
discussion of the stationary distribution on, as well as of the stationary flow
across each space. We demonstrate that optimizing the flow is equivalent to
minimizing the first passage time for crossing the space, and discuss the
consequences of our results for optimizing simulations. Finally, we point out
the limitations of these representations under conditions of broken ergodicity.Comment: 11 pages Latex, 2 eps figures, revised version, typos corrected, PRE
in pres
Deconfinement Transition and Bound States in Frustrated Heisenberg Chains: Regimes of Forced and Spontaneous Dimerization
We use recently developed strong-coupling expansion methods to study the
two-particle spectra for the frustrated alternating Heisenberg model,
consisting of an alternating nearest neighbor antiferromagnetic exchange and a
uniform second neighbor antiferromagnetic exchange. Starting from the limit of
weakly coupled dimers, we develop high order series expansions for the
effective Hamiltonian in the two-particle subspace. In the limit of a strong
applied dimerization, we calculate accurately various properties of singlet and
triplet bound states and quintet antibound states. We also develop series
expansions for bound state energies in various sectors, which can be
extrapolated using standard methods to cases where the external
bond-alternation goes to zero. We study the properties of singlet and triplet
bound states in the latter limit and suggest a crucial role for the bound
states in the unbinding of triplets and deconfinement of spin-half excitations.Comment: 17 figures, revte
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