1,157 research outputs found
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
and can be solved exactly by Quantum Monte Carlo methods. We argue
that, for reasonable 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
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