206 research outputs found
Violation of the Luttinger sum rule within the Hubbard model on a triangular lattice
The frequency-moment expansion method is developed to analyze the validity of
the Luttinger sum rule within the Mott-Hubbard insulator, as represented by the
generalized Hubbard model at half filling and large . For the particular
case of the Hubbard model with nearest-neighbor hopping on a triangular lattice
lacking the particle-hole symmetry results reveal substantial violation of the
sum rule.Comment: 4 pages, 2 figure
Bound states in two spatial dimensions in the non-central case
We derive a bound on the total number of negative energy bound states in a
potential in two spatial dimensions by using an adaptation of the Schwinger
method to derive the Birman-Schwinger bound in three dimensions. Specifically,
counting the number of bound states in a potential gV for g=1 is replaced by
counting the number of g_i's for which zero energy bound states exist, and then
the kernel of the integral equation for the zero-energy wave functon is
symmetrized. One of the keys of the solution is the replacement of an
inhomogeneous integral equation by a homogeneous integral equation.Comment: Work supported in part by the U.S. Department of Energy under Grant
No. DE-FG02-84-ER4015
Bosonization of the Low Energy Excitations of Fermi Liquids
We bosonize the low energy excitations of Fermi Liquids in any number of
dimensions in the limit of long wavelengths. The bosons are coherent
superposition of electron-hole pairs and are related with the displacement of
the Fermi Surface in some arbitrary direction. A coherent-state path integral
for the bosonized theory is derived and it is shown to represent histories of
the shape of the Fermi Surface. The Landau equation for the sound waves is
shown to be exact in the semiclassical approximation for the bosons.Comment: 10 pages, RevteX, P-93-03-027 (UIUC
Two-dimensional array of magnetic particles: The role of an interaction cutoff
Based on theoretical results and simulations, in two-dimensional arrangements
of a dense dipolar particle system, there are two relevant local dipole
arrangements: (1) a ferromagnetic state with dipoles organized in a triangular
lattice, and (2) an anti-ferromagnetic state with dipoles organized in a square
lattice. In order to accelerate simulation algorithms we search for the
possibility of cutting off the interaction potential. Simulations on a dipolar
two-line system lead to the observation that the ferromagnetic state is much
more sensitive to the interaction cutoff than the corresponding
anti-ferromagnetic state. For (measured in particle diameters)
there is no substantial change in the energetical balance of the ferromagnetic
and anti-ferromagnetic state and the ferromagnetic state slightly dominates
over the anti-ferromagnetic state, while the situation is changed rapidly for
lower interaction cutoff values, leading to the disappearance of the
ferromagnetic ground state. We studied the effect of bending ferromagnetic and
anti-ferromagnetic two-line systems and we observed that the cutoff has a major
impact on the energetical balance of the ferromagnetic and anti-ferromagnetic
state for . Based on our results we argue that is a
reasonable choice for dipole-dipole interaction cutoff in two-dimensional
dipolar hard sphere systems, if one is interested in local ordering.Comment: 8 page
Hall Coefficient in an Interacting Electron Gas
The Hall conductivity in a weak homogeneous magnetic field, , is calculated. We have shown that to leading order in
the Hall coefficient is not renormalized by the
electron-electron interaction. Our result explains the experimentally observed
stability of the Hall coefficient in a dilute electron gas not too close to the
metal-insulator transition. We avoid the currently used procedure that
introduces an artificial spatial modulation of the magnetic field. The problem
of the Hall effect is reformulated in a way such that the magnetic flux
associated with the scattering process becomes the central element of the
calculation.Comment: 23 pages, 15 figure
A second eigenvalue bound for the Dirichlet Schroedinger operator
Let be the th eigenvalue of the Schr\"odinger
operator with Dirichlet boundary conditions on a bounded domain and with the positive potential . Following the spirit of the
Payne-P\'olya-Weinberger conjecture and under some convexity assumptions on the
spherically rearranged potential , we prove that . Here denotes the ball, centered at the
origin, that satisfies the condition .
Further we prove under the same convexity assumptions on a spherically
symmetric potential , that decreases
when the radius of the ball increases.
We conclude with several results about the first two eigenvalues of the
Laplace operator with respect to a measure of Gaussian or inverted Gaussian
density
An Exact Diagonalization Demonstration of Incommensurability and Rigid Band Filling for N Holes in the t-J Model
We have calculated S(q) and the single particle distribution function
for N holes in the t - J model on a non--square sqrt{8} X sqrt{32} 16--site
lattice with periodic boundary conditions; we justify the use of this lattice
in compariosn to those of having the full square symmetry of the bulk. This new
cluster has a high density of vec k points along the diagonal of reciprocal
space, viz. along k = (k,k). The results clearly demonstrate that when the
single hole problem has a ground state with a system momentum of vec k =
(pi/2,pi/2), the resulting ground state for N holes involves a shift of the
peak of the system's structure factor away from the antiferromagnetic state.
This shift effectively increases continuously with N. When the single hole
problem has a ground state with a momentum that is not equal to k =
(pi/2,pi/2), then the above--mentioned incommensurability for N holes is not
found. The results for the incommensurate ground states can be understood in
terms of rigid--band filling: the effective occupation of the single hole k =
(pi/2,pi/2) states is demonstrated by the evaluation of the single particle
momentum distribution function . Unlike many previous studies, we show
that for the many hole ground state the occupied momentum states are indeed k =
(+/- pi/2,+/- pi/2) states.Comment: Revtex 3.0; 23 pages, 1 table, and 13 figures, all include
Field-Driven Transitions in the Dipolar Pyrochlore Antiferromagnet GdTiO
We present a mean-field theory for magnetic field driven transitions in
dipolar coupled gadolinium titanate GdTiO pyrochlore system. Low
temperature neutron scattering yields a phase that can be regarded as a 8
sublattice antiferromagnet, in which long-ranged ordered moments and
fluctuating moments coexist. Our theory gives parameter regions where such a
phase is realized, and predicts several other phases, with transitions amongst
them driven by magnetic field as well as temperature. We find several instances
of {\em local} disorder parameters describing the transitions.Comment: 4 pages, 5 figures. v2: longer version with 2 add.fig., to appear in
PR
Two-dimensional dilute Bose gas in the normal phase
We consider a two-dimensional dilute Bose gas above its superfluid transition
temperature. We show that the t-matrix approximation corresponds to the leading
set of diagrams in the dilute limit, provided the temperature is sufficiently
larger than the superfluid transition temperature. Within this approximation,
we give an explicit expression for the wave vector and frequency dependence of
the self-energy, and calculate the corrections to the chemical potential and
the effective mass arising from the interaction. We also argue that the
breakdown of the t-matrix approximation, which occurs upon lowering the
temperature, provides a simple criterion to estimate the superfluid critical
temperature for the two-dimensional dilute Bose gas. The critical temperature
identified by this criterion coincides with earlier results obtained by Popov
and by Fisher and Hohenberg using different methods. Extension of this
procedure to the three-dimensional case gives good agreement with recent Monte
Carlo data.Comment: 9 pages, 3 Figure
Diagrammatic self-energy approximations and the total particle number
There is increasing interest in many-body perturbation theory as a practical tool for the calculation of ground-state properties. As a consequence, unambiguous sum rules such as the conservation of particle number under the influence of the Coulomb interaction have acquired an importance that did not exist for calculations of excited-state properties. In this paper we obtain a rigorous, simple relation whose fulfilment guarantees particle-number conservation in a given diagrammatic self-energy approximation. Hedin's G(0)W(0) approximation does not satisfy this relation and hence violates the particle-number sum rule. Very precise calculations for the homogeneous electron gas and a model inhomogeneous electron system allow the extent of the nonconservation to be estimated
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