64 research outputs found
Interacting electrons in a two-dimensional disordered environment: Effect of a Zeeman magnetic field
The effect of a Zeeman magnetic field coupled to the spin of the electrons on
the conducting properties of the disordered Hubbard model is studied. Using the
Determinant Quantum Monte Carlo method, the temperature- and magnetic-field-
dependent conductivity is calculated,as well as the degree of spin
polarization. We find that the Zeeman magnetic field suppresses the metallic
behavior present for certain values of interaction- and disorder- strength, and
is able to induce a metal-insulator transition at a critical field strength. It
is argued that the qualitative features of magnetoconductance in this
microscopic model containing both repulsive interactions and disorder are in
agreement with experimental findings in two-dimensional electron- and
hole-gases in semiconductor structures.Comment: 4 pages, 4 figure
Determinant Quantum Monte Carlo Study of the Screening of the One Body Potential near a Metal-Insulator Transition
In this paper we present a determinant quantum monte carlo study of the two
dimensional Hubbard model with random site disorder. We show that, as in the
case of bond disorder, the system undergoes a transition from an Anderson
insulating phase to a metallic phase as the onsite repulsion U is increased
beyond a critical value U_c. However, there appears to be no sharp signal of
this metal-insulator transition in the screened site energies. We observe that,
while the system remains metallic for interaction values upto twice U_c, the
conductivity is maximal in the metallic phase just beyond U_c, and decreases
for larger correlation.Comment: 6 pages, 10 eps figures, Revtex
Ordered states in the disordered Hubbard model
The Hubbard model is studied in which disorder is introduced by putting the
on-site interaction to zero on a fraction f of (impurity) sites of a square
lattice. Using Quantum Monte Carlo methods and Dynamical Mean Field theory we
find that antiferromagnetic long-range order is initially enhanced at
half-filling and stabilized off half-filling by the disorder. The Mott-Hubbard
charge gap of the pure system is broken up into two pieces by the disorder: one
incompressible state remains at average density n=1 and another can be seen
slightly below n=1+f. Qualitative explanations are provided.Comment: 17 pages, including 8 figures. Paper for Festschrift in honor of Hans
van Leeuwen's 65th birthda
Dynamic response of trapped ultracold bosons on optical lattices
We study the dynamic response of ultracold bosons trapped in one-dimensional
optical lattices using Quantum Monte Carlo simulations of the boson Hubbard
model with a confining potential. The dynamic structure factor reveals the
inhomogeneous nature of the low temperature state, which contains coexisting
Mott insulator and superfluid regions. We present new evidence for local
quantum criticality and shed new light on the experimental excitation spectrum
of 87Rb atoms confined in one dimension.Comment: 4 pages, 5 figure
Phase coherence, visibility, and the superfluid--Mott-insulator transition on one-dimensional optical lattices
We study the phase coherence and visibility of trapped atomic condensates on
one-dimensional optical lattices, by means of quantum Monte-Carlo simulations.
We obtain structures in the visibility similar to the kinks recently observed
experimentally by Gerbier et.al.[Phy. Rev. Lett. 95, 050404 (2005); Phys. Rev.
A 72, 053606 (2005)]. We examine these features in detail and offer a
connection to the evolution of the density profiles as the depth of the lattice
is increased. Our simulations reveal that as the interaction strength, U, is
increased, the evolution of superfluid and Mott-insulating domains stall for
finite intervals of U. The density profiles do not change with increasing U. We
show here that in one dimension the visibility provides unequivocal signatures
of the melting of Mott domains with densities larger than one.Comment: 4 pages, 5 figure
Superfluid and Mott Insulator phases of one-dimensional Bose-Fermi mixtures
We study the ground state phases of Bose-Fermi mixtures in one-dimensional
optical lattices with quantum Monte Carlo simulations using the Canonical Worm
algorithm. Depending on the filling of bosons and fermions, and the on-site
intra- and inter-species interaction, different kinds of incompressible and
superfluid phases appear. On the compressible side, correlations between bosons
and fermions can lead to a distinctive behavior of the bosonic superfluid
density and the fermionic stiffness, as well as of the equal-time Green
functions, which allow one to identify regions where the two species exhibit
anticorrelated flow. We present here complete phase diagrams for these systems
at different fillings and as a function of the interaction parameters.Comment: 8 pages, 12 figure
Mott Domains of Bosons Confined on Optical Lattices
In the absence of a confining potential, the boson Hubbard model in its
ground state is known to exhibit a superfluid to Mott insulator quantum phase
transition at commensurate fillings and strong on-site repulsion. In this
paper, we use quantum Monte Carlo simulations to study the ground state of the
one dimensional bosonic Hubbard model in a trap. We show that some, but not
all, aspects of the Mott insulating phase persist when a confining potential is
present. The Mott behavior is present for a continuous range of incommensurate
fillings, a very different situation from the unconfined case. Furthermore the
establishment of the Mott phase does not proceed via a quantum phase transition
in the traditional sense. These observations have important implications for
the interpretation of experimental results for atoms trapped on optical
lattices. Initial results show that, qualitatively, the same results persist in
higher dimensions.Comment: Revtex file, five figures, include
Critical temperature for the two-dimensional attractive Hubbard Model
The critical temperature for the attractive Hubbard model on a square lattice
is determined from the analysis of two independent quantities, the helicity
modulus, , and the pairing correlation function, . These
quantities have been calculated through Quantum Monte Carlo simulations for
lattices up to , and for several densities, in the
intermediate-coupling regime. Imposing the universal-jump condition for an
accurately calculated , together with thorough finite-size scaling
analyses (in the spirit of the phenomenological renormalization group) of
, suggests that is considerably higher than hitherto assumed.Comment: 5 pages, 6 figures. Accepted for publication in Phys. Rev.
Particle-Hole Symmetry and the Effect of Disorder on the Mott-Hubbard Insulator
Recent experiments have emphasized that our understanding of the interplay of
electron correlations and randomness in solids is still incomplete. We address
this important issue and demonstrate that particle-hole (ph) symmetry plays a
crucial role in determining the effects of disorder on the transport and
thermodynamic properties of the half-filled Hubbard Hamiltonian. We show that
the low-temperature conductivity decreases with increasing disorder when
ph-symmetry is preserved, and shows the opposite behavior, i.e. conductivity
increases with increasing disorder, when ph-symmetry is broken. The Mott
insulating gap is insensitive to weak disorder when there is ph-symmetry,
whereas in its absence the gap diminishes with increasing disorder.Comment: 4 pages, 4 figure
The random disc thrower problem
We describe a number of approaches to a question posed by Philips Research, described as the "random disc thrower" problem. Given a square grid of points in the plane, we cover the points by equal-sized planar discs according to the following random process. At each step, a random point of the grid is chosen from the set of uncovered points as the centre of a new disc. This is an abstract model of spatial reuse in wireless networks. A question of Philips Research asks what, as a function of the grid length, is the expected number of discs chosen before the process can no longer continue? Our main results concern the one-dimensional variant of this problem, which can be solved reasonably well, though we also provide a number of approaches towards an approximate solution of the original two-dimensional problem. The two-dimensional problem is related to an old, unresolved conjecture ([6]) that has been the object of close study in both probability theory and statistical physics. Keywords: generating functions, Markov random fields, random sequential adsorption, Rényi’s parking problem, wireless network
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