Effective hamiltonian approach for strongly correlated lattice models

We review a recent approach for the simulation of many-body interacting systems based on an efficient generalization of the Lanczos method for Quantum Monte Carlo simulations. This technique allows to perform systematic corrections to a given variational wavefunction, that allow to estimate exact energies and correlation functions, whenever the starting variational wavefunction is a qualitatively correct description of the ground state. The stability of the variational wavefunction against possible phases, not described at the variational level can be tested by using the ''effective Hamiltonian'' approach. In fact Monte Carlo methods, such as the ''fixed node approximation'' and the ''generalized Lanczos technique'' (Phys. Rev. B 64,024512, 2001) allow to obtain exact ground state properties of an effective Hamiltonian, chosen to be as close as possible to the exact Hamiltonian, thus yielding the most reasonable estimates of correlation functions. We also describe a simplified one-parameter scheme that improve substantially the efficiency of the generalized Lanczos method. This is tested on the t-J model, with a special effort to obtain accurate pairing correlations, and provide a possible non-phonon mechanism for High temperature superconductivity.Comment: 19 pages, 7 colour figures, lecture notes for the Euro Winter School-Kerkrade-N

Wave function optimization in the variational Monte Carlo method

An 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 1D Heisenberg ring and the 2D 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.Comment: 5 pages, 3 figures, to be published in Phys. Rev B (Rapid Comm.

Do Bose metals exist in Nature?

We revisit the concept of superfluidity in bosonic lattice models in low dimensions. Then, by using numerical and analytical results obtained previously for equivalent spinless fermion models, we show that the gapless phase of 1D interacting bosons may be either superfluid or -remarkably- metallic and not superfluid. The latter phase -the Bose metal- should be, according to the mentioned results, a robust and stable phase in 1D. In higher dimensionalities we speculate on the possibility of a stable Bose metallic phase on the verge of a Mott transition.Comment: 12 pages, 2 figures, to appear in the proceedings of the Peyres conferenc

Linearized Auxiliary fields Monte Carlo: efficient sampling of the fermion sign

We introduce a method that combines the power of both the lattice Green function Monte Carlo (LGFMC) with the auxiliary field techniques (AFQMC), 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 exp(- H t). On the other hand the AFQMC formalism yields a remarkably fast convergence in t before the fermion sign problem becomes prohibitive. As a first application we report ground state energies in the Hubbard model at U/t=4 with up to one hundred sites.Comment: 5 pages, 3 figure

Remarks on the dynamical mass generation in confining Yang-Mills theories

The dynamical mass generation for gluons is discussed in Euclidean Yang-Mills theories supplemented with a renormalizable mass term. The mass parameter is not free, being determined in a self-consistent way through a gap equation which obeys the renormalization group. The example of the Landau gauge is worked out explicitly at one loop order. A few remarks on the issue of the unitarity are provided.Comment: 11 pages, final version to appear in Brazilian Journal of Physic

Effective hamiltonian approach and the lattice fixed node approximation

We define a numerical scheme that allows to approximate a given Hamiltonian by an effective one, by requiring several constraints determined by exact properties of generic ''short range'' Hamiltonians. In this way the standard lattice fixed node is also improved as far as the variational energy is concerned. The effective Hamiltonian is defined in terms of a guiding function $\psi_G$ and can be solved exactly by Quantum Monte Carlo methods. We argue that, for reasonable $\psi_G$ and away from phase transitions, the long distance, low energy properties are rather independent on the chosen guiding function, thus allowing to remove the well known problem of standard variational Monte Carlo schemes based only on total energy minimizations, and therefore insensitive to long distance low energy properties.Comment: 8 pages, for the proceedings of "The Monte Carlo Method in the Physical Sciences: Celebrating the 50th Anniversary of the Metropolis Algorithm", Los Alamos, June 9-11, 200