246 research outputs found
Superfluid to Mott insulator transition in the one-dimensional Bose-Hubbard model for arbitrary integer filling factors
We study the quantum phase transition between the superfluid and the Mott
insulator in the one-dimensional (1D) Bose-Hubbard model. Using the
time-evolving block decimation method, we numerically calculate the tunneling
splitting of two macroscopically distinct states with different winding
numbers. From the scaling of the tunneling splitting with respect to the system
size, we determine the critical point of the superfluid to Mott insulator
transition for arbitrary integer filling factors. We find that the critical
values versus the filling factor in 1D, 2D, and 3D are well approximated by a
simple analytical function. We also discuss the condition for determining the
transition point from a perspective of the instanton method.Comment: 6 pages, 6 figures, 2 table
W_\infty and w_\infty Gauge Theories and Contraction
We present a general method of constructing Winf and winf gauge theories in
terms of d+2 dimensional local fields. In this formulation the \Winf gauge
theory Lagrangians involve non-local interactions, but the winf theories are
entirely local. We discuss the so-called classical contraction procedure by
which we derive the Lagrangian of winf gauge theory from that of the
corresponding Winf gauge theory. In order to discuss the relationship between
quantum Winf and quantum winf gauge theory we solve d=1 gauge theory models of
a Higgs field exactly by using the collective field method. Based on this we
conclude that the Winf gauge theory can be regarded as the large N limit of the
corresponding SU(N) gauge theory once an appropriate coupling constant
renormalization is made, while the winf gauge theory cannot be.Comment: 21 pages, plain Te
Self Consistent Field Method for Planar phi^3 Theory
We continue and extend earlier work on the summation of planar graphs in
phi^3 field theory, based on a local action on the world sheet. The present
work employs a somewhat different version of the self consistent field
(meanfield) approximation compared to the previous work on the same subject.
Using this new approach, we are able to determine in general the asymptotic
forms of the solutions, and in the case of one solution, even its exact form.
This solution leads to formation of an unstable string, in agreement with the
previous work. We also investigate and clarify questions related to Lorentz
invariance and the renormalization of the solution.Comment: Latex, no other macros neede
Further Results about Field Theory on the World Sheet and String Formation
The present article is the continuation of the earlier work, which used the
world sheet representation and the mean field approximation to sum planar
graphs in massless phi^3 field theory. We improve on the previous work in two
respects: A prefactor in the world sheet propagator that had been neglected is
now taken into account. In addition, we introduce a non-zero bare mass for the
field phi. Working with a theory with cutoff, and using the mean field
approximation, we find that, depending on the range of values of the mass and
coupling constant, the model has two phases: A string forming phase and a
perturbative field theory phase. We also find the generation of a new degree of
freedom, which was not in the model originally. The new degree of freedom can
be thought of as the string slope, which is now promoted into a fluctuating
dynamical variable. Finally, we show that the introduction of the bare mass
makes it possible to renormalize the model.Comment: 39 pages, 10 figures, typos corrected and one equation simplifie
More On The Connection Between Planar Field Theory And String Theory
We continue work on the connection between world sheet representation of the
planar phi^3 theory and string formation. The present article, like the earlier
work, is based on the existence of a solitonic solution on the world sheet, and
on the zero mode fluctuations around this solution. The main advance made in
this paper is the removal of the cutoff and the transition to the continuum
limit on the world sheet. The result is an action for the modes whose energies
remain finite in this limit (light modes). The expansion of this action about a
dense background of graphs on the world sheet leads to the formation of a
string.Comment: 27 pages, 3 figure
Equivalence of Two Dimensional QCD and the Matrix Model
We consider two dimensional QCD with the spatial dimension compactified to a
circle. We show that the states in the theory consist of interacting strings
that wind around the circle and derive the Hamiltonian for this theory in the
large limit, complete with interactions. Mapping the winding states into
momentum states, we express this Hamiltonian in terms of a continuous field.
For a gauge group with a background source of Wilson loops, we recover
the collective field Hamiltonian found by Das and Jevicki for the matrix
model, except the spatial coordinate is on a circle. We then proceed to show
that two dimensional QCD with a gauge group can be reduced to a one-
dimensional unitary matrix model and is hence equivalent to a theory of
free nonrelativistic fermions on a circle. A similar result is true for the
group , but the fermions must be modded out by the center of mass
coordinate.Comment: 15 pages, CERN-TH 6843/93, UVA-HET-93-0
Solitons and excitations in the duality-based matrix model
We analyse a specific, duality-based generalization of the hermitean matrix
model. The existence of two collective fields enables us to describe specific
excitations of the hermitean matrix model. By using these two fields, we
construct topologically non-trivial solutions (BPS solitons) of the model. We
find the low-energy spectrum of quantum fluctuations around the uniform
solution. Furthermore, we construct the wave functional of the ground state and
obtain the corresponding Green function.Comment: 13 pages,v2: new solutions constructed, title changed accordingl
Quantum phase slips in one-dimensional superfluids in a periodic potential
We study the decay of superflow of a one-dimensional (1D) superfluid in the
presence of a periodic potential. In 1D, superflow at zero temperature can
decay via quantum nucleation of phase slips even when the flow velocity is much
smaller than the critical velocity predicted by mean-field theories. Applying
the instanton method to the O(2) quantum rotor model, we calculate the
nucleation rate of quantum phase slips . When the flow momentum is
small, we find that the nucleation rate per unit length increases algebraically
with as , where is the system size and
is the Tomonaga-Luttinger parameter. Based on the relation between the
nucleation rate and the quantum superfluid-insulator transition, we present a
unified explanation on the scaling formulae of the nucleation rate for
periodic, disorder, and single-barrier potentials. Using the time-evolving
block decimation method, we compute the exact quantum dynamics of the superflow
decay in the 1D Bose-Hubbard model at unit filling. From the numerical
analyses, we show that the scaling formula is valid for the case of the
Bose-Hubbard model, which can quantitatively describe Bose gases in optical
lattices.Comment: 11 pages, 8 figures, Sec. V is adde
Field Theory On The World Sheet: Improvements And Generalizations
This article is the continuation of a project of investigating planar phi^3
model in various dimensions. The idea is to reformulate them on the world
sheet, and then to apply the classical (meanfield) approximation, with two
goals: To show that the ground state of the model is a solitonic configuration
on the world sheet, and the quantum fluctuations around the soliton lead to the
formation of a transverse string. After a review of some of the earlier work,
we introduce and discuss several generalizations and new results. In 1+2
dimensions, a rigorous upper bound on the solitonic energy is established. A
phi^4 interaction is added to stabilize the original phi^3 model. In 1+3 and
1+5 dimensions, an improved treatment of the ultraviolet divergences is given.
And significantly, we show that our approximation scheme can be imbedded into a
systematic strong coupling expansion. Finally, the spectrum of quantum
fluctuations around the soliton confirms earlier results: In 1+2 and 1+3
dimensions, a transverse string is formed on the world sheet.Comment: 29 pages, 5 figures, several typos and eqs.(74) and (75) are
corrected, a comment added to section
Fluctuation effects of gauge fields in the slave-boson t-J model
We present a quantitative study of the charge-spin separation(CSS) phenomenon
in a U(1) gauge theory of the t-J model of high-Tc superconductures. We
calculate the critical temperature of confinement-deconfinement phase
transition below which the CSS takes place.Comment: Latex, 9 pages, 3 figure
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