Function Monte Carlo Technique Research Articles

Gapless spin-liquid phase in the kagome spin-12Heisenberg antiferromagnet

We study the energy and the static spin structure factor of the ground state of the spin-$1/2$ quantum Heisenberg antiferromagnetic model on the kagome lattice. By the iterative application of a few Lanczos steps on accurate projected fermionic wave functions and the Green's function Monte Carlo technique, we find that a gapless (algebraic) $U(1)$ Dirac spin liquid is competitive with previously proposed gapped (topological) ${\mathbb{Z}}_{2}$ spin liquids. By performing a finite-size extrapolation of the ground-state energy, we obtain an energy per site $E/J=\ensuremath{-}0.4365(2)$, which is equal, within three error bars, to the estimates given by the density-matrix renormalization group (DMRG). Our estimate is obtained for a translationally invariant system, and, therefore, does not suffer from boundary effects, like in DMRG. Moreover, on finite toric clusters at the pure variational level, our energies are lower compared to those from DMRG calculations.

Generic Mixed Columnar-Plaquette Phases in Rokhsar-Kivelson Models

We revisit the phase diagram of Rokhsar-Kivelson models, which are used in fields such as superconductivity, frustrated magnetism, cold bosons, and the physics of Josephson junction arrays. From an extended height effective theory, we show that one of two simple generic phase diagrams contains a mixed phase that interpolates continuously between columnar and plaquette states. For the square lattice quantum dimer model we present evidence from exact diagonalization and Green's function Monte Carlo techniques that this scenario is realized, by combining an analysis of the excitation gaps of different symmetry sectors with information on plaquette structure factors. This presents a natural framework for resolving the disagreement between previous studies.

Ground state of coupled spin-half ladders

The ground state of an array of coupled, spin-half, antiferromagnetic ladders is studied using the Green's function Monte Carlo technique. Our results clearly indicate the occurrence of a zero-temperature phase transition between a Néel ordered and a non-magnetic phase at a finite value of the inter-ladder coupling ( α c≃0.3). This transition is marked by remarkable changes in the structure of the excitation spectrum.

Charge Fluctuations Close to Phase Separation in the Two-Dimensionalt−JModel

We have studied the $t\ensuremath{-}J$ model using the Green function Monte Carlo technique. We have obtained accurate energies well converged in the thermodynamic limit by performing simulations for up to $242$ lattice sites. By studying the energy as a function of hole doping we conclude that there is no phase separation in the physical region relevant for high- ${T}_{c}$ superconductors. This finding is further supported by the hole-hole correlation function calculation. Remarkably, near the phase separation instability, for ${J}_{c}/t\ensuremath{\sim}0.5$ this function displays enhanced fluctuations at incommensurate wave vectors that scale linearly with the doping, in agreement with experimental findings.

Green Function Monte Carlo with Stochastic Reconfiguration

A new method for the stabilization of the sign problem in the Green Function Monte Carlo technique is proposed. The method is devised for real lattice Hamiltonians and is based on an iterative ''stochastic reconfiguration'' scheme which introduces some bias but allows a stable simulation with constant sign. The systematic reduction of this bias is in principle possible. The method is applied to the frustrated J1-J2 Heisenberg model, and tested against exact diagonalization data. Evidence of a finite spin gap for J2/J1 >~ 0.4 is found in the thermodynamic limit.

Numerical study of the two-dimensional Heisenberg model using a Green function Monte Carlo technique with a fixed number of walkers

We describe in detail a simple and efficient Green function Monte Carlo technique for computing both the ground state energy and the ground state properties by the ``forward walking'' scheme. The simplicity of our reconfiguration process, used to maintain the walker population constant, allows us to control any source of systematic error in a rigorous and systematic way. We apply this method to the Heisenberg model and obtain accurate and reliable estimates of the ground state energy, the order parameter, and the static spin structure factor $S(q)$ for several momenta. For the latter quantity we also find very good agreement with available experimental data on the ${\mathrm{La}}_{2}{\mathrm{CuO}}_{4}$ antiferromagnet.

Quantum Monte Carlo study of the one-dimensional Holstein model of spinless fermions.

The Holstein model of spinless fermions interacting with dispersionless phonons in one dimension is studied by a Green's function Monte Carlo technique. The ground state energy, first fermionic excited state, density wave correlations, and mean lattice displacement are calculated for lattices of up to 16 sites, for one fermion per two sites, i.e., a half-filled band. Results are obtained for values of the fermion hopping parameter of $t=0.1 \omega$, $\omega$, and $10 \omega$ where $\omega$ is the phonon frequency. At a finite fermion-phonon coupling $g$ there is a transition from a metallic phase to an insulating phase in which there is charge-density-wave order. Finite size scaling is found to hold in the metallic phase and is used to extract the coupling dependence of the Luttinger liquid parameters, $u_\rho$ and $K_\rho$, the velocity of charge excitations and the correlation exponent, respectively. For free fermions ($g=0$) and for strong coupling ($g^2 \gg t \omega$) our results agree well with known analytic results. For $t=\omega$ and $t=10\omega$ our results are inconsistent with the metal-insulator transition being a Kosterlitz-Thouless transition.\\

Application of parquet perturbation theory to ground states of boson systems.

In the interest of polishing the parquet approach to microscopic calculations of ground-state properties of zero-temperature quantum fluids, we have developed a perturbative scheme for the systematic improvement of the four-point function which retains the correct behavior of the parquet diagrams in both the small-r and small-k limits. Numerical implementation of this scheme indicates significantly improved agreement with binding energies calculated with Green's-function Monte Carlo techniques (i.e., differences in liquid $^{4}\mathrm{He}$ are less than 1.5%). The charged Bose gas and the hard-sphere system are also considered. Remaining difficulties in the calculations of the liquid structure function are noted and discussed.