57 research outputs found
Lieb-Schultz-Mattis in Higher Dimensions
A generalization of the Lieb-Schultz-Mattis theorem to higher dimensional
spin systems is shown. The physical motivation for the result is that such spin
systems typically either have long-range order, in which case there are gapless
modes, or have only short-range correlations, in which case there are
topological excitations. The result uses a set of loop operators, analogous to
those used in gauge theories, defined in terms of the spin operators of the
theory. We also obtain various cluster bounds on expectation values for gapped
systems. These bounds are used, under the assumption of a gap, to rule out the
first case of long-range order, after which we show the existence of a
topological excitation. Compared to the ground state, the topologically excited
state has, up to a small error, the same expectation values for all operators
acting within any local region, but it has a different momentum.Comment: 14 pages, 3 figures, final version in pres
The Flux-Phase of the Half-Filled Band
The conjecture is verified that the optimum, energy minimizing magnetic flux
for a half-filled band of electrons hopping on a planar, bipartite graph is
per square plaquette. We require {\it only} that the graph has
periodicity in one direction and the result includes the hexagonal lattice
(with flux 0 per hexagon) as a special case. The theorem goes beyond previous
conjectures in several ways: (1) It does not assume, a-priori, that all
plaquettes have the same flux (as in Hofstadter's model); (2) A Hubbard type
on-site interaction of any sign, as well as certain longer range interactions,
can be included; (3) The conclusion holds for positive temperature as well as
the ground state; (4) The results hold in dimensions if there is
periodicity in directions (e.g., the cubic lattice has the lowest energy
if there is flux in each square face).Comment: 9 pages, EHL14/Aug/9
Pocket Monte Carlo algorithm for classical doped dimer models
We study the correlations of classical hardcore dimer models doped with
monomers by Monte Carlo simulation. We introduce an efficient cluster
algorithm, which is applicable in any dimension, for different lattices and
arbitrary doping. We use this algorithm for the dimer model on the square
lattice, where a finite density of monomers destroys the critical confinement
of the two-monomer problem. The monomers form a two-component plasma located in
its high-temperature phase, with the Coulomb interaction screened at finite
densities. On the triangular lattice, a single pair of monomers is not
confined. The monomer correlations are extremely short-ranged and hardly change
with doping.Comment: 6 pages, REVTeX
Mott insulators in strong electric fields
Recent experiments on ultracold atomic gases in an optical lattice potential
have produced a Mott insulating state of Rb atoms. This state is stable to a
small applied potential gradient (an `electric' field), but a resonant response
was observed when the potential energy drop per lattice spacing (E), was close
to the repulsive interaction energy (U) between two atoms in the same lattice
potential well. We identify all states which are resonantly coupled to the Mott
insulator for E close to U via an infinitesimal tunneling amplitude between
neighboring potential wells. The strong correlation between these states is
described by an effective Hamiltonian for the resonant subspace. This
Hamiltonian exhibits quantum phase transitions associated with an Ising density
wave order, and with the appearance of superfluidity in the directions
transverse to the electric field. We suggest that the observed resonant
response is related to these transitions, and propose experiments to directly
detect the order parameters. The generalizations to electric fields applied in
different directions, and to a variety of lattices, should allow study of
numerous other correlated quantum phases.Comment: 17 pages, 14 figures; (v2) minor additions and new reference
A planar diagram approach to the correlation problem
We transpose an idea of 't Hooft from its context of Yang and Mills' theory
of strongly interacting quarks to that of strongly correlated electrons in
transition metal oxides and show that a Hubbard model of N interacting electron
species reduces, to leading orders in N, to a sum of almost planar diagrams.
The resulting generating functional and integral equations are very similar to
those of the FLEX approximation of Bickers and Scalapino. This adds the Hubbard
model at large N to the list of solvable models of strongly correlated
electrons.
PACS Numbers: 71.27.+a 71.10.-w 71.10.FdComment: revtex, 5 pages, with 3 eps figure
Asymptotics of block Toeplitz determinants and the classical dimer model
We compute the asymptotics of a block Toeplitz determinant which arises in
the classical dimer model for the triangular lattice when considering the
monomer-monomer correlation function. The model depends on a parameter
interpolating between the square lattice () and the triangular lattice
(), and we obtain the asymptotics for . For we apply the
Szeg\"o Limit Theorem for block Toeplitz determinants. The main difficulty is
to evaluate the constant term in the asymptotics, which is generally given only
in a rather abstract form
Splitting of a doubly quantized vortex through intertwining in Bose-Einstein condensates
The stability of doubly quantized vortices in dilute Bose-Einstein
condensates of 23Na is examined at zero temperature. The eigenmode spectrum of
the Bogoliubov equations for a harmonically trapped cigar-shaped condensate is
computed and it is found that the doubly quantized vortex is spectrally
unstable towards dissection into two singly quantized vortices. By numerically
solving the full three-dimensional time-dependent Gross-Pitaevskii equation, it
is found that the two singly quantized vortices intertwine before decaying.
This work provides an interpretation of recent experiments [A. E. Leanhardt et
al. Phys. Rev. Lett. 89, 190403 (2002)].Comment: 4 pages, 3 figures (to be published in PRA
A maximum density rule for surfaces of quasicrystals
A rule due to Bravais of wide validity for crystals is that their surfaces
correspond to the densest planes of atoms in the bulk of the material.
Comparing a theoretical model of i-AlPdMn with experimental results, we find
that this correspondence breaks down and that surfaces parallel to the densest
planes in the bulk are not the most stable, i.e. they are not so-called bulk
terminations. The correspondence can be restored by recognizing that there is a
contribution to the surface not just from one geometrical plane but from a
layer of stacked atoms, possibly containing more than one plane. We find that
not only does the stability of high-symmetry surfaces match the density of the
corresponding layer-like bulk terminations but the exact spacings between
surface terraces and their degree of pittedness may be determined by a simple
analysis of the density of layers predicted by the bulk geometric model.Comment: 8 pages of ps-file, 3 Figs (jpg
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