1,721,127 research outputs found
Linearized auxiliary fields Monte Carlo technique: Efficient sampling of the fermion sign
No full textWe introduce a method that combines the power of both the lattice Green' function Monte Carlo (LGFMC) with the auxiliary field quantum Monte Carlo (AFQMC) techniques, and allows us to compute exact ground-state properties of the Hubbard model for U≲4t on finite clusters. Thanks to LGFMC, one obtains unbiased zero temperature results, not affected by the so-called Trotter approximation of the imaginary time propagator e−Hτ. At the same time, the AFQMC formalism yields a remarkably fast convergence in τ before the fermion sign problem becomes prohibitive. As an application we report ground-state energies of the Hubbard model at U/t=4 with up to 100 sites
Sharp photoemission spectra in the quantum antiferromagnet
No full textThe low energy photoemission spectra in quantum antiferromagnets are studied by using several approximation-free calculations and rigorous theorems. The important and measurable property found is that the hole eigenstates with momenta differing by the antiferromagnetic wave vector Q are equivalent and degenerate in energy. However, the corresponding eigenstates differ by the presence or the absence of a well-defined quasiparticle corresponding to a singular. zero-energy, magnon, carrying spin one and momentum Q. This difference between the two eigenstates affects dramatically the spectral weight as a function of the scattered momentum, since a sharp effect at the surface of the magnetic Brillouin zone is predicted, in apparent agreement with recent experimental data
Numerical evidence of Luttinger- and Fermi-liquid behavior in the two-dimensional Hubbard model
No full textThe two-dimensional Hubbard model with a single spin-up electron interacting with a finite density of spin-down electrons is studied by use of the quantum Monte Carlo technique, the standard second-order perturbation theory and a very good variational wave function introduced recently by Edwards. We also present a new conjugate gradient scheme for the evaluation of this variational state. We performed simulations up to 242 sites at U/t = 4 reaching the zero-temperature properties with no ''fermion-sign problem'' and found a surprisingly good accuracy of the Edwards state at low density or low doping. The conjugate gradient method was then applied to the system up to 3698 sites and infinite U. Fermi-liquid theory seems to remain stable in two dimensions for all cases studied with the exception of the half-filling case where a Luttinger-like behavior survives in the Hubbard model, yielding a vanishing quasiparticle weight in the thermodynamic limit
Quantum Monte Carlo study of a single hole in a quantum antiferromagnet
No full textUsing the standard quantum Monte Carlo technique for the Hubbard model, I present here a numerical investigation of the hole propagation in a quantum antiferromagnet. The calculation is very well stabilized, using selected-size systems and a special choice of the trial wave function that satisfies the "closed-shell condition" in the presence of an arbitrarily weak Zeeman magnetic field. First it is shown that the presence of this magnetic field does not affect the thermodynamic properties of the half-filled system. Then I use the same selected sizes for the one-hole ground state. I investigate the question of vanishing or nonvanishing quasiparticle weight, in order to clarify whether the Mott insulator behaves as a conventional insulator with an upper and lower Hubbard band. By comparing the present finite-size scaling with several techniques that predict a finite quasiparticle weight, the data seem more consistent with a vanishing quasiparticle weight, i.e., the Mott-Hubbard insulator should be characterized by nontrivial excitations that cannot be interpreted in a simple picture. However, one cannot exclude, based only on numerical grounds, a very small but nonvanishing quasiparticle weight. In the last part I give some theoretical arguments to explain the results of the Monte Carlo simulation
Wave function optimization in the variational Monte Carlo method
No full textAn appropriate iterative scheme for the minimization of the energy, based on the variational Monte Carlo (VMC) technique, is introduced and compared with existing stochastic schemes. We test the various methods for the one-dimensional Heisenberg ring and the two-dimensional t-J model and show that, with the present scheme, very accurate and efficient calculations are possible, even for several variational parameters. Indeed, by using a very efficient statistical evaluation of the first and the second energy derivatives, it is possible to define a very rapidly converging iterative scheme that, within VMC, is much more convenient than the standard Newton method. It is also shown how to optimize simultaneously both the Jastrow and the determinantal part of the wave function
Green function monte carlo with stochastic reconfiguration
No full textA 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 possible in principle. 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
On the classification of the low energy excitations in the doped antiferromagnet
No full textA long-wavelength, low energy hamiltonian is derived to describe the dynamic of a single hole in a quantum antiferromagnet in two or higher spatial dimensions. In this exactly solvable limit a new kind of symmetry is important to classify the elementary spin excitations of a single hole in the t - J model. This symmetry is hidden at finite size or at short wavelength. The resulting classification has important consequences for understanding the physics of doped antiferromagnets. Fermi liquid like s = 1/2 and charge one excitations are still well defined in a quantum antiferromagnet, but are not a complete set to describe the low energy physics
Generalized lanczos algorithm for variational quantum Monte Carlo
No full textWe show that the standard Lanczos algorithm can be efficiently implemented statistically and self-consistently improved, using the stochastic reconfiguration method, which has been recently introduced to stabilize the Monte Carlo sign problem instability. With this scheme a few Lanczos steps over a given variational wave function are possible even for large size as a particular case of a more general and more accurate technique that allows to obtain lower variational energies. This method has been tested extensively for a strongly correlated model like the t-J model. With the standard Lanczos technique it is possible to compute any kind of correlation functions, with no particular computational effort. By using the fact that the variance <H-2>-<H > (2) is zero for an exact eigenstate, we show that the approach to the exact solution with few Lonczos iterations is indeed possible even for similar to 100 electrons for reasonably good initial wave functions. The variational stochastic reconfiguration technique presented here allows in general a many-parameter energy optimization of any computable many-body wave function, including for instance generic long-range Jastrow factors and arbitrary site-dependent orbital determinants. This scheme improves further the accuracy of the calculation, especially for long-distance correlation functions
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