Sign Rules for Anisotropic Quantum Spin Systems

We present new and exact ``sign rules'' for various spin-s anisotropic spin-lattice models. It is shown that, after a simple transformation which utilizes these sign rules, the ground-state wave function of the transformed Hamiltonian is positive-definite. Using these results exact statements for various expectation values of off-diagonal operators are presented, and transitions in the behavior of these expectation values are observed at particular values of the anisotropy. Furthermore, the effects of sign rules in variational calculations and quantum Monte Carlo calculations are considered. They are illustrated by a simple variational treatment of a one-dimensional anisotropic spin model.Comment: 4 pages, 1 ps-figur

Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems

We report several important observations that underscore the distinctions between the constrained-path Monte Carlo method and the continuum and lattice versions of the fixed-node method. The main distinctions stem from the differences in the state space in which the random walk occurs and in the manner in which the random walkers are constrained. One consequence is that in the constrained-path method the so-called mixed estimator for the energy is not an upper bound to the exact energy, as previously claimed. Several ways of producing an energy upper bound are given, and relevant methodological aspects are illustrated with simple examples.Comment: 28 pages, REVTEX, 5 ps figure

An Improved Upper Bound for the Ground State Energy of Fermion Lattice Models

We present an improved upper bound for the ground state energy of lattice fermion models with sign problem. The bound can be computed by numerical simulation of a recently proposed family of deformed Hamiltonians with no sign problem. For one dimensional models, we expect the bound to be particularly effective and practical extrapolation procedures are discussed. In particular, in a model of spinless interacting fermions and in the Hubbard model at various filling and Coulomb repulsion we show how such techniques can estimate ground state energies and correlation function with great accuracy.Comment: 5 pages, 5 figures; to appear in Physical Review

From antiferromagnetism to d-wave superconductivity in the 2D t-J model

We have found that the two dimensional t-J model, for the physical parameter range J/t = 0.4 reproduces the main experimental qualitative features of High-Tc copper oxide superconductors: d-wave superconducting correlations are strongly enhanced upon small doping and clear evidence of off diagonal long range order is found at the optimal doping \delta ~ 0.15. On the other hand antiferromagnetic long range order, clearly present at zero hole doping, is suppressed at small hole density with clear absence of antiferromagnetism at \delta >~ 0.1.Comment: 4 pages, 5 figure

Incorporation of Density Matrix Wavefunctions in Monte Carlo Simulations: Application to the Frustrated Heisenberg Model

We combine the Density Matrix Technique (DMRG) with Green Function Monte Carlo (GFMC) simulations. The DMRG is most successful in 1-dimensional systems and can only be extended to 2-dimensional systems for strips of limited width. GFMC is not restricted to low dimensions but is limited by the efficiency of the sampling. This limitation is crucial when the system exhibits a so-called sign problem, which on the other hand is not a particular obstacle for the DMRG. We show how to combine the virtues of both methods by using a DMRG wavefunction as guiding wave function for the GFMC. This requires a special representation of the DMRG wavefunction to make the simulations possible within reasonable computational time. As a test case we apply the method to the 2-dimensional frustrated Heisenberg antiferromagnet. By supplementing the branching in GFMC with Stochastic Reconfiguration (SR) we get a stable simulation with a small variance also in the region where the fluctuations due to minus sign problem are maximal. The sensitivity of the results to the choice of the guiding wavefunction is extensively investigated. We analyse the model as a function of the ratio of the next-nearest to nearest neighbor coupling strength. We observe in the frustrated regime a pattern of the spin correlations which is in-between dimerlike and plaquette type ordering, states that have recently been suggested. It is a state with strong dimerization in one direction and weaker dimerization in the perpendicular direction.Comment: slightly revised version with added reference

Mott Transition in Degenerate Hubbard Models: Application to Doped Fullerenes

The Mott-Hubbard transition is studied for a Hubbard model with orbital degeneracy N, using a diffusion Monte-Carlo method. Based on general arguments, we conjecture that the Mott-Hubbard transition takes place for U/W \propto \sqrt{N}, where U is the Coulomb interaction and W is the band width. This is supported by exact diagonalization and Monte-Carlo calculations. Realistic parameters for the doped fullerenes lead to the conclusion that stoichiometric A_3 C_60 (A=K, Rb) are near the Mott-Hubbard transition, in a correlated metallic state.Comment: 4 pages, revtex, 1 eps figure included, to be published in Phys.Rev.B Rapid Com

Spatially homogeneous ground state of the two-dimensional Hubbard model

We investigate the stability with respect to phase separation or charge density-wave formation of the two-dimensional Hubbard model for various values of the local Coulomb repulsion and electron densities using Green-function Monte Carlo techniques. The well known sign problem is particularly serious in the relevant region of small hole doping. We show that the difference in accuracy for different doping makes it very difficult to probe the phase separation instability using only energy calculations, even in the weak-coupling limit ($U=4t$) where reliable results are available. By contrast, the knowledge of the charge correlation functions allows us to provide clear evidence of a spatially homogeneous ground state up to $U=10t$.Comment: 7 pages and 5 figures. Phys. Rev. B, to appear 200

Random Exchange Quantum Heisenberg Chains

The one-dimensional quantum Heisenberg model with random $\pm J$ bonds is studied for $S=\frac{1}{2}$ and $S=1$. The specific heat and the zero-field susceptibility are calculated by using high-temperature series expansions and quantum transfer matrix method. The susceptibility shows a Curie-like temperature dependence at low temperatures as well as at high temperatures. The numerical results for the specific heat suggest that there are anomalously many low-lying excitations. The qualitative nature of these excitations is discussed based on the exact diagonalization of finite size systems.Comment: 13 pages, RevTex, 12 figures available on request ([email protected]

A quantum Monte Carlo study of the one-dimensional ionic Hubbard model

Quantum Monte Carlo methods are used to study a quantum phase transition in a 1D Hubbard model with a staggered ionic potential (D). Using recently formulated methods, the electronic polarization and localization are determined directly from the correlated ground state wavefunction and compared to results of previous work using exact diagonalization and Hartree-Fock. We find that the model undergoes a thermodynamic transition from a band insulator (BI) to a broken-symmetry bond ordered (BO) phase as the ratio of U/D is increased. Since it is known that at D = 0 the usual Hubbard model is a Mott insulator (MI) with no long-range order, we have searched for a second transition to this state by (i) increasing U at fixed ionic potential (D) and (ii) decreasing D at fixed U. We find no transition from the BO to MI state, and we propose that the MI state in 1D is unstable to bond ordering under the addition of any finite ionic potential. In real 1D systems the symmetric MI phase is never stable and the transition is from a symmetric BI phase to a dimerized BO phase, with a metallic point at the transition

Low-temperature behavior of the large-U Hubbard model from high-temperature expansions

We derive low-temperature properties of the large-U Hubbard model in two and three dimensions starting from exact series-expansion results for high temperatures. Convergence problems and limited available information prevent a direct or Padé-type extrapolation. We propose a method of extrapolation, which is restricted to large U and low hole densities, for which the problem can be mapped on that of a system of weakly interacting holes. In this formulation an extrapolation down to T=0 can be obtained, but it can be trusted for the presently available series data for βt≲20 and for hole densities nh≲0.2 only. Implications for the magnetic phase diagram are discussed.Theoretical Physic