Pairing Correlations in the Two-Dimensional Hubbard Model

We present the results of a quantum Monte Carlo study of the extended $s$ and the $d_{x^2-y^2}$ 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 $d_{x^2-y^2}$ pairing correlations are stronger than the extended $s$ 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 $|\Psi_T \rangle$, we remove the exponential decay of signal-to-noise ratio characteristic of the sign problem. The method is variational and is exact if $|\Psi_T\rangle$ is exact. We report results on the two-dimensional Hubbard model up to size $16\times 16$, 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-$U$ 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.

Two-dimensional Superfluidity and Localization in the Hard-Core Boson Model: a Quantum Monte Carlo Study

Quantum Monte Carlo simulations are used to investigate the two-dimensional superfluid properties of the hard-core boson model, which show a strong dependence on particle density and disorder. We obtain further evidence that a half-filled clean system becomes superfluid via a finite temperature Kosterlitz-Thouless transition. The relationship between low temperature superfluid density and particle density is symmetric and appears parabolic about the half filling point. Disorder appears to break the superfluid phase up into two distinct localized states, depending on the particle density. We find that these results strongly correlate with the results of several experiments on high-$T_c$ superconductors.Comment: 10 pages, 3 figures upon request, RevTeX version 3, (accepted for Phys. Rev. B

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

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