44 research outputs found
Fixed-Node Monte Carlo Calculations for the 1d Kondo Lattice Model
The effectiveness of the recently developed Fixed-Node Quantum Monte Carlo
method for lattice fermions, developed by van Leeuwen and co-workers, is tested
by applying it to the 1D Kondo lattice, an example of a one-dimensional model
with a sign problem. The principles of this method and its implementation for
the Kondo Lattice Model are discussed in detail. We compare the fixed-node
upper bound for the ground state energy at half filling with
exact-diagonalization results from the literature, and determine several spin
correlation functions. Our `best estimates' for the ground state correlation
functions do not depend sensitively on the input trial wave function of the
fixed-node projection, and are reasonably close to the exact values. We also
calculate the spin gap of the model with the Fixed-Node Monte Carlo method. For
this it is necessary to use a many-Slater-determinant trial state. The
lowest-energy spin excitation is a running spin soliton with wave number pi, in
agreement with earlier calculations.Comment: 19 pages, revtex, contribution to Festschrift for Hans van Leeuwe
Stripes and spin-incommensurabilities are favored by lattice anisotropies
Structural distortions in cuprate materials give a natural origin for
anisotropies in electron properties. We study a modified one-band t-J model in
which we allow for different hoppings and antiferromagnetic couplings in the
two spatial directions ( and ). Incommensurate peaks
in the spin structure factor show up only in the presence of a lattice
anisotropy, whereas charge correlations, indicating enhanced fluctuations at
incommensurate wave vectors, are almost unaffected with respect to the
isotropic case.Comment: accepted for publication on Physical Review Letters, one color figur
Helicity Modulus and Effective Hopping in the Two-Dimensional Hubbard Model Using Slave-Boson Methods
The slave-boson mean-field method is used to study the two-dimensional
Hubbard model. A magnetic phase diagram allowing for paramagnetism, weak- and
strong ferromagnetism and antiferromagnetism, including all continuous and
first-order transitions, is constructed and compared to the corresponding phase
diagram using the Hartree-Fock approximation (HFA). Magnetically ordered
regions are reduced by a factor of about 3 along both the and density
axes compared to the HFA. Using the spin-rotation invariant formulation of the
slave-boson method the helicity modulus is computed and for half-filling is
found to practically coincide with that found using variational Monte Carlo
calculations using the Gutzwiller wave function. Off half-filling the results
can be used to compare with Quantum Monte Carlo calculations of the effective
hopping parameter. Contrary to the case of half-filling, the slave-boson
approach is seen to greatly improve the results of the HFA when off
half-filling. (Submitted to: Journal of Physics: Condensed Matter)Comment: 27 pages, LaTeX2e, 7 figures available upon request, INLO-PUB-10/9
Proof for an upper bound in fixed-node Monte Carlo for lattice fermions
We justify a recently proposed prescription for performing Green Function
Monte Carlo calculations on systems of lattice fermions, by which one is able
to avoid the sign problem. We generalize the prescription such that it can also
be used for problems with hopping terms of different signs. We prove that the
effective Hamiltonian, used in this method, leads to an upper bound for the
ground-state energy of the real Hamiltonian, and we illustrate the
effectiveness of the method on small systems.Comment: 14 pages in revtex v3.0, no figure
Charge fluctuations close to phase separation in the two dimensional t-J model
We have studied the t-J model using the Green Function Monte Carlo technique.
We have obtained accurate energies well converged in the thermodynamic limit,
by performing simulations 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 HTc superconductors. This finding is further
supported by the hole-hole correlation function calculation. Remarkably, by
approaching the phase separation instability, for ,this function
displays enhanced fluctuations at incommensurate wavevectors, scaling linearly
with the doping, in agreement with experimental findings.Comment: To appear on Phys. Rev. Let
Superconductivity in the two-dimensional t-J model
Using computational techniques, it is shown that pairing is a robust property
of hole doped antiferromagnetic (AF) insulators. In one dimension (1D) and for
two-leg ladder systems, a BCS-like variational wave function with long-bond
spin-singlets and a Jastrow factor provides an accurate representation of the
ground state of the t-J model, even though strong quantum fluctuations destroy
the off-diagonal superconducting (SC) long-range order in this case. However,
in two dimensions (2D) it is argued -- and numerically confirmed using several
techniques, especially quantum Monte Carlo (QMC) -- that quantum fluctuations
are not strong enough to suppress superconductivity.Comment: 4 pages, 5 figure
Spontaneous plaquette dimerization in the Heisenberg model
We investigate the non magnetic phase of the spin-half frustrated Heisenberg
antiferromagnet on the square lattice using exact diagonalization (up to 36
sites) and quantum Monte Carlo techniques (up to 144 sites). The spin gap and
the susceptibilities for the most important crystal symmetry breaking operators
are computed. A genuine and somehow unexpected `plaquette RVB', with
spontaneously broken translation symmetry and no broken rotation symmetry,
comes out from our numerical simulations as the most plausible ground state for
.Comment: 4 pages, 5 postscript figure
Green's Function Monte Carlo for Lattice Fermions: Application to the t-J Model
We develop a general numerical method to study the zero temperature
properties of strongly correlated electron models on large lattices. The
technique, which resembles Green's Function Monte Carlo, projects the ground
state component from a trial wave function with no approximations. We use this
method to determine the phase diagram of the two-dimensional t-J model, using
the Maxwell construction to investigate electronic phase separation. The shell
effects of fermions on finite-sized periodic lattices are minimized by keeping
the number of electrons fixed at a closed-shell configuration and varying the
size of the lattice. Results obtained for various electron numbers
corresponding to different closed-shells indicate that the finite-size effects
in our calculation are small. For any value of interaction strength, we find
that there is always a value of the electron density above which the system can
lower its energy by forming a two-component phase separated state. Our results
are compared with other calculations on the t-J model. We find that the most
accurate results are consistent with phase separation at all interaction
strengths.Comment: 22 pages, 22 figure
Long range Neel order in the triangular Heisenberg model
We have studied the Heisenberg model on the triangular lattice using several
Quantum Monte Carlo (QMC) techniques (up to 144 sites), and exact
diagonalization (ED) (up to 36 sites). By studying the spin gap as a function
of the system size we have obtained a robust evidence for a gapless spectrum,
confirming the existence of long range Neel order. Our best estimate is that in
the thermodynamic limit the order parameter m= 0.41 +/- 0.02 is reduced by
about 59% from its classical value and the ground state energy per site is
e0=-0.5458 +/- 0.0001 in unit of the exchange coupling. We have identified the
important ground state correlations at short distance.Comment: 4 pages, RevTeX + 4 encapsulated postscript figure