Numerical Study of a Two-Dimensional Quantum Antiferromagnet with Random Ferromagnetic Bonds

A Monte Carlo method for finite-temperature studies of the two-dimensional quantum Heisenberg antiferromagnet with random ferromagnetic bonds is presented. The scheme is based on an approximation which allows for an analytic summation over the realizations of the randomness, thereby significantly alleviating the ``sign problem'' for this frustrated spin system. The approximation is shown to be very accurate for ferromagnetic bond concentrations of up to ten percent. The effects of a low concentration of ferromagnetic bonds on the antiferromagnetism are discussed.Comment: 11 pages + 5 postscript figures (included), Revtex 3.0, UCSBTH-94-2

Simulating `Complex' Problems with Quantum Monte Carlo

We present a new quantum Monte Carlo algorithm suitable for generically complex problems, such as systems coupled to external magnetic fields or anyons in two spatial dimensions. We find that the choice of gauge plays a nontrivial role, and can be used to reduce statistical noise in the simulation. Furthermore, it is found that noise can be greatly reduced by approximate cancellations between the phases of the (gauge dependent) statistical flux and the external magnetic flux.Comment: Revtex, 11 pages. 3 postscript files for figures attache

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

Adaptive Sampling Approach to the Negative Sign Problem in the Auxiliary Field Quantum Monte Carlo Method

We propose a new sampling method to calculate the ground state of interacting quantum systems. This method, which we call the adaptive sampling quantum monte carlo (ASQMC) method utilises information from the high temperature density matrix derived from the monte carlo steps. With the ASQMC method, the negative sign ratio is greatly reduced and it becomes zero in the limit $\Delta \tau$ goes to zero even without imposing any constraint such like the constraint path (CP) condition. Comparisons with numerical results obtained by using other methods are made and we find the ASQMC method gives accurate results over wide regions of physical parameters values.Comment: 8 pages, 7 figure

The Hubbard model with smooth boundary conditions

We apply recently developed smooth boundary conditions to the quantum Monte Carlo simulation of the two-dimensional Hubbard model. At half-filling, where there is no sign problem, we show that the thermodynamic limit is reached more rapidly with smooth rather than with periodic or open boundary conditions. Away from half-filling, where ordinarily the simulation cannot be carried out at low temperatures due to the existence of the sign problem, we show that smooth boundary conditions allow us to reach significantly lower temperatures. We examine pairing correlation functions away from half-filling in order to determine the possible existence of a superconducting state. On a $10\times 10$ lattice for $U=4$, at a filling of $\langle n \rangle = 0.87$ and an inverse temperature of $\beta=10$, we did find enhancement of the $d$-wave correlations with respect to the non-interacting case, a possible sign of $d$-wave superconductivity.Comment: 16 pages RevTeX, 9 postscript figures included (Figure 1 will be faxed on request

The sign problem in Monte Carlo simulations of frustrated quantum spin systems

We discuss the sign problem arising in Monte Carlo simulations of frustrated quantum spin systems. We show that for a class of ``semi-frustrated'' systems (Heisenberg models with ferromagnetic couplings $J_z(r) < 0$ along the $z$-axis and antiferromagnetic couplings $J_{xy}(r)=-J_z(r)$ in the $xy$-plane, for arbitrary distances $r$) the sign problem present for algorithms operating in the $z$-basis can be solved within a recent ``operator-loop'' formulation of the stochastic series expansion method (a cluster algorithm for sampling the diagonal matrix elements of the power series expansion of ${\rm exp}(-\beta H)$ to all orders). The solution relies on identification of operator-loops which change the configuration sign when updated (``merons'') and is similar to the meron-cluster algorithm recently proposed by Chandrasekharan and Wiese for solving the sign problem for a class of fermion models (Phys. Rev. Lett. {\bf 83}, 3116 (1999)). Some important expectation values, e.g., the internal energy, can be evaluated in the subspace with no merons, where the weight function is positive definite. Calculations of other expectation values require sampling of configurations with only a small number of merons (typically zero or two), with an accompanying sign problem which is not serious. We also discuss problems which arise in applying the meron concept to more general quantum spin models with frustrated interactions.Comment: 13 pages, 16 figure

Effects of domain walls on hole motion in the two-dimensional t-J model at finite temperature

The t-J model on the square lattice, close to the t-J_z limit, is studied by quantum Monte Carlo techniques at finite temperature and in the underdoped regime. A variant of the Hoshen-Koppelman algorithm was implemented to identify the antiferromagnetic domains on each Trotter slice. The results show that the model presents at high enough temperature finite antiferromagnetic (AF) domains which collapse at lower temperatures into a single ordered AF state. While there are domains, holes would tend to preferentially move along the domain walls. In this case, there are indications of hole pairing starting at a relatively high temperature. At lower temperatures, when the whole system becomes essentially fully AF ordered, at least in finite clusters, holes would likely tend to move within phase separated regions. The crossover between both states moves down in temperature as doping increases and/or as the off-diagonal exchange increases. The possibility of hole motion along AF domain walls at zero temperature in the fully isotropic t-J is discussed.Comment: final version, to appear in Physical Review

Two-magnon Raman scattering in insulating cuprates: Modifications of the effective Raman operator

Calculations of Raman scattering intensities in spin 1/2 square-lattice Heisenberg model, using the Fleury-Loudon-Elliott theory, have so far been unable to describe the broad line shape and asymmetry of the two magnon peak found experimentally in the cuprate materials. Even more notably, the polarization selection rules are violated with respect to the Fleury-Loudon-Elliott theory. There is comparable scattering in $B_{1g}$ and $A_{1g}$ geometries, whereas the theory would predict scattering in only $B_{1g}$ geometry. We review various suggestions for this discrepency and suggest that at least part of the problem can be addressed by modifying the effective Raman Hamiltonian, allowing for two-magnon states with arbitrary total momentum. Such an approach based on the Sawatzsky-Lorenzana theory of optical absorption assumes an important role of phonons as momentum sinks. It leaves the low energy physics of the Heisenberg model unchanged but substantially alters the Raman line-shape and selection rules, bringing the results closer to experiments.Comment: 7 pages, 6 figures, revtex. Contains some minor revisions from previous versio

Supersymmetry breaking in two dimensions: the lattice N=1 Wess-Zumino model

We study dynamical supersymmetry breaking by non perturbative lattice techniques in a class of two-dimensional N=1 Wess-Zumino models. We work in the Hamiltonian formalism and analyze the phase diagram by analytical strong-coupling expansions and explicit numerical simulations with Green Function Monte Carlo methods.Comment: 53 pages, 17 figures, revtex

Low-temperature dynamical simulation of spin-boson systems

The dynamics of spin-boson systems at very low temperatures has been studied using a real-time path-integral simulation technique which combines a stochastic Monte Carlo sampling over the quantum fluctuations with an exact treatment of the quasiclassical degrees of freedoms. To a large degree, this special technique circumvents the dynamical sign problem and allows the dynamics to be studied directly up to long real times in a numerically exact manner. This method has been applied to two important problems: (1) crossover from nonadiabatic to adiabatic behavior in electron transfer reactions, (2) the zero-temperature dynamics in the antiferromagnetic Kondo region 1/2<K<1 where K is Kondo's parameter.Comment: Phys. Rev. B (in press), 28 pages, 6 figure