1,329 research outputs found
Pairing Correlations in the Two-Dimensional Hubbard Model
We present the results of a quantum Monte Carlo study of the extended and
the pairing correlation functions for the two-dimensional Hubbard
model, computed with the constrained-path method. For small lattice sizes and
weak interactions, we find that the pairing correlations are
stronger than the extended pairing correlations and are positive when the
pair separation exceeds several lattice constants. As the system size or the
interaction strength increases, the magnitude of the long-range part of both
correlation functions vanishes.Comment: 4 pages, RevTex, 4 figures included; submitted to Phys. Rev. Let
Evolution of pairing from weak to strong coupling on a honeycomb lattice
We study the evolution of the pairing from weak to strong coupling on a
honeycomb lattice by Quantum Monte Carlo. We show numerical evidence of the
BCS-BEC crossover as the coupling strength increases on a honeycomb lattice
with small fermi surface by measuring a wide range of observables: double
occupancy, spin susceptibility, local pair correlation, and kinetic energy.
Although at low energy, the model sustains Dirac fermions, we do not find
significant qualitative difference in the BCS-BEC crossover as compared to
those with an extended Fermi surface, except at weak coupling, BCS regime.Comment: 5 page
A Constrained Path Quantum Monte Carlo Method for Fermion Ground States
We propose a new quantum Monte Carlo algorithm to compute fermion
ground-state properties. The ground state is projected from an initial
wavefunction by a branching random walk in an over-complete basis space of
Slater determinants. By constraining the determinants according to a trial
wavefunction , we remove the exponential decay of
signal-to-noise ratio characteristic of the sign problem. The method is
variational and is exact if is exact. We report results on the
two-dimensional Hubbard model up to size , for various electron
fillings and interaction strengths.Comment: uuencoded compressed postscript file. 5 pages with 1 figure. accepted
by PRL
Finite-Temperature Monte Carlo Calculations For Systems With Fermions
We present a quantum Monte Carlo method which allows calculations on
many-fermion systems at finite temperatures without any sign decay. This
enables simulations of the grand-canonical ensemble at large system sizes and
low temperatures. Both diagonal and off-diagonal expectations can be computed
straightforwardly. The sign decay is eliminated by a constraint on the fermion
determinant. The algorithm is approximate. Tests on the Hubbard model show that
accurate results on the energy and correlation functions can be obtained.Comment: 5 pages, RevTex; to appear in Phys. Rev. Let
Practical solution to the Monte Carlo sign problem: Realistic calculations of 54Fe
We present a practical solution to the "sign problem" in the auxiliary field
Monte Carlo approach to the nuclear shell model. The method is based on
extrapolation from a continuous family of problem-free Hamiltonians. To
demonstrate the resultant ability to treat large shell-model problems, we
present results for 54Fe in the full fp-shell basis using the Brown-Richter
interaction. We find the Gamow-Teller beta^+ strength to be quenched by 58%
relative to the single-particle estimate, in better agreement with experiment
than previous estimates based on truncated bases.Comment: 11 pages + 2 figures (not included
Loop algorithms for quantum simulations of fermion models on lattices
Two cluster algorithms, based on constructing and flipping loops, are
presented for worldline quantum Monte Carlo simulations of fermions and are
tested on the one-dimensional repulsive Hubbard model. We call these algorithms
the loop-flip and loop-exchange algorithms. For these two algorithms and the
standard worldline algorithm, we calculated the autocorrelation times for
various physical quantities and found that the ordinary worldline algorithm,
which uses only local moves, suffers from very long correlation times that
makes not only the estimate of the error difficult but also the estimate of the
average values themselves difficult. These difficulties are especially severe
in the low-temperature, large- regime. In contrast, we find that new
algorithms, when used alone or in combinations with themselves and the standard
algorithm, can have significantly smaller autocorrelation times, in some cases
being smaller by three orders of magnitude. The new algorithms, which use
non-local moves, are discussed from the point of view of a general prescription
for developing cluster algorithms. The loop-flip algorithm is also shown to be
ergodic and to belong to the grand canonical ensemble. Extensions to other
models and higher dimensions is briefly discussed.Comment: 36 pages, RevTex ver.
A Two-dimensional Infinte System Density Matrix Renormalization Group Algorithm
It has proved difficult to extend the density matrix renormalization group
technique to large two-dimensional systems. In this Communication I present a
novel approach where the calculation is done directly in two dimensions. This
makes it possible to use an infinite system method, and for the first time the
fixed point in two dimensions is studied. By analyzing several related blocking
schemes I find that there exists an algorithm for which the local energy
decreases monotonically as the system size increases, thereby showing the
potential feasibility of this method.Comment: 5 pages, 6 figure
Multiple Histogram Method for Quantum Monte Carlo
An extension to the multiple-histogram method (sometimes referred to as the
Ferrenberg-Swendsen method) for use in quantum Monte Carlo simulations is
presented. This method is shown to work well for the 2D repulsive Hubbard
model, allowing measurements to be taken over a continuous region of
parameters. The method also reduces the error bars over the range of parameter
values due the overlapping of multiple histograms. A continuous sweep of
parameters and reduced error bars allow one to make more difficult
measurements, such as Maxwell constructions used to study phase separation.
Possibilities also exist for this method to be used for other quantum systems.Comment: 4 pages, 5 figures, RevTeX, submitted to Phys. Rev. B Rapid Com
Multilevel blocking approach to the fermion sign problem in path-integral Monte Carlo simulations
A general algorithm toward the solution of the fermion sign problem in
finite-temperature quantum Monte Carlo simulations has been formulated for
discretized fermion path integrals with nearest-neighbor interactions in the
Trotter direction. This multilevel approach systematically implements a simple
blocking strategy in a recursive manner to synthesize the sign cancellations
among different fermionic paths throughout the whole configuration space. The
practical usefulness of the method is demonstrated for interacting electrons in
a quantum dot.Comment: 4 pages RevTeX, incl. two figure
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