637 research outputs found
Phase diagram of the bose Hubbard model
The first reliable analytic calculation of the phase diagram of the bose gas
on a -dimensional lattice with on-site repulsion is presented. In one
dimension, the analytic calculation is in excellent agreement with the
numerical Monte Carlo results. In higher dimensions, the deviations from the
Monte Carlo calculations are larger, but the correct shape of the Mott
insulator lobes is still obtained. Explicit expressions for the energy of the
Mott and the ``defect'' phase are given in a strong-coupling expansion.Comment: RevTeX 3.
Study of the charge correlation function in one-dimensional Hubbard heterostructures
We study inhomogeneous one-dimensional Hubbard systems using the density
matrix renormalization group method. Different heterostructures are
investigated whose configuration is modeled varying parameters like the on-site
Coulomb potential and introducing local confining potentials. We investigate
their Luttinger liquid properties through the parameter K_rho, which
characterizes the decay of the density-density correlation function at large
distances. Our main goal is the investigation of possible realization of
engineered materials and the ability to manipulate physical properties by
choosing an appropriate spatial and/or chemical modulation.Comment: 6 pages, 7 figure
Lattice susceptibility for 2D Hubbard Model within dual fermion method
In this paper, we present details of the dual fermion (DF) method to study
the non-local correction to single site DMFT. The DMFT two-particle Green's
function is calculated using continuous time quantum monte carlo (CT-QMC)
method. The momentum dependence of the vertex function is analyzed and its
renormalization based on the Bethe-Salpeter equation is performed in
particle-hole channel. We found a magnetic instability in both the dual and the
lattice fermions. The lattice fermion susceptibility is calculated at finite
temperature in this method and also in another recently proposed method, namely
dynamical vertex approximation (DA). The comparison between these two
methods are presented in both weak and strong coupling region. Compared to the
susceptibility from quantum monte carlo (QMC) simulation, both of them gave
satisfied results.Comment: 10 pages, 11 figure
Fictive Impurity Approach to Dynamical Mean Field Theory: a Strong-Coupling Investigation
Quantum Monte Carlo and semiclassical methods are used to solve two and four
site cluster dynamical mean field approximations to the square lattice Hubbard
model at half filling and strong coupling. The energy, spin correlation
function, phase boundary and electron spectral function are computed and
compared to available exact results. The comparision permits a quantitative
assessment of the ability of the different methods to capture the effects of
intersite spin correlations. Two real space methods and one momentum space
representation are investigated. One of the two real space methods is found to
be significantly worse: in it, convergence to the correct results is found to
be slow and, for the spectral function, nonuniform in frequency, with
unphysical midgap states appearing. Analytical arguments are presented showing
that the discrepancy arises because the method does not respect the pole
structure of the self energy of the insulator. Of the other two methods, the
momentum space representation is found to provide the better approximation to
the intersite terms in the energy but neither approximation is particularly
acccurate and the convergence of the momentum space method is not uniform. A
few remarks on numerical methods are made.Comment: Errors in previous versions corrected; CDMFT results adde
Spin-charge separation in ultra-cold quantum gases
We investigate the physical properties of quasi-1D quantum gases of fermion
atoms confined in harmonic traps. Using the fact that for a homogeneous gas,
the low energy properties are exactly described by a Luttinger model, we
analyze the nature and manifestations of the spin-charge separation. Finally we
discuss the necessary physical conditions and experimental limitations
confronting possible experimental implementations.Comment: 4 pages, revtex4, 2 eps figure
Finding the Minimum-Weight k-Path
Given a weighted -vertex graph with integer edge-weights taken from a
range , we show that the minimum-weight simple path visiting
vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k
M). If the weights are reals in , we provide a
-approximation which has a running time of \tilde{O}(2^k
\poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem
of -tree, in which we wish to find a minimum-weight copy of a -node tree
in a given weighted graph , under the same restrictions on edge weights
respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k)
M n^3) and a -approximate solution of running time
\tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above
algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201
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