630 research outputs found
Application of a multi-site mean-field theory to the disordered Bose-Hubbard model
We present a multi-site formulation of mean-field theory applied to the
disordered Bose-Hubbard model. In this approach the lattice is partitioned into
clusters, each isolated cluster being treated exactly, with inter-cluster
hopping being treated approximately. The theory allows for the possibility of a
different superfluid order parameter at every site in the lattice, such as what
has been used in previously published site-decoupled mean-field theories, but a
multi-site formulation also allows for the inclusion of spatial correlations
allowing us, e.g., to calculate the correlation length (over the length scale
of each cluster). We present our numerical results for a two-dimensional
system. This theory is shown to produce a phase diagram in which the stability
of the Mott insulator phase is larger than that predicted by site-decoupled
single-site mean-field theory. Two different methods are given for the
identification of the Bose glass-to-superfluid transition, one an approximation
based on the behaviour of the condensate fraction, and one of which relies on
obtaining the spatial variation of the order parameter correlation. The
relation of our results to a recent proposal that both transitions are non
self-averaging is discussed.Comment: Accepted for publication in Physical Review
Multi-site mean-field theory for cold bosonic atoms in optical lattices
We present a detailed derivation of a multi-site mean-field theory (MSMFT)
used to describe the Mott-insulator to superfluid transition of bosonic atoms
in optical lattices. The approach is based on partitioning the lattice into
small clusters which are decoupled by means of a mean field approximation. This
approximation invokes local superfluid order parameters defined for each of the
boundary sites of the cluster. The resulting MSMFT grand potential has a
non-trivial topology as a function of the various order parameters. An
understanding of this topology provides two different criteria for the
determination of the Mott insulator superfluid phase boundaries. We apply this
formalism to -dimensional hypercubic lattices in one, two and three
dimensions, and demonstrate the improvement in the estimation of the phase
boundaries when MSMFT is utilized for increasingly larger clusters, with the
best quantitative agreement found for . The MSMFT is then used to examine
a linear dimer chain in which the on-site energies within the dimer have an
energy separation of . This system has a complicated phase diagram
within the parameter space of the model, with many distinct Mott phases
separated by superfluid regions.Comment: 30 pages, 23 figures, accepted for publication in Phys. Rev.
Dynamical Gauge Symmetry Breaking and Superconductivity in three-dimensional systems
We discuss dynamical breaking of non-abelian gauge groups in three
dimensional (lattice) gauge systems via the formation of fermion condensates. A
physically relevant example, motivated by condensed-matter physics, is that of
a fermionic gauge theory with group . In
the strong U_S(1) region, the SU(2) symmetry breaks down to a U(1), due to the
formation of a parity-invariant fermion condensate. We conjecture a phase
diagram for the theory involving a critical line, which separates the regions
of broken SU(2) symmetry from those where the symmetry is restored. In the
broken phase, the effective Abelian gauge theory is closely related to an
earlier model of two-dimensional parity-invariant superconductivity in doped
antiferromagnets. The superconductivity in the model occurs in the
Kosterlitz-Thouless mode, since strong phase fluctuations prevent the existence
of a local order parameter. Some physical consequences of the phase diagram for the (doping-dependent) parameter space of this
condensed-matter model are briefly discussed.Comment: 17 pages Latex, 1 macro, three figures (included) (minor typo on page
14 concerning the critical coupling of SU(2) corrected
Possibility of spontaneous parity violation in hot QCD
We suggest that for QCD in the limit of a large number of colors, N, the
axial U(1) symmetry of massless quarks is effectively restored at the
deconfining=chiral phase transition. If the deconfining transition is of second
order, then the chiral transition is weakly first order. In this case,
metastable states in which parity is spontaneously broken appear at
temperatures below the phase transition. The production of these metastable
states would have dramatic signatures, including enhanced production of eta and
eta' mesons, which can decay through parity violating decay processes such as
eta -> pi^0 pi^0, and global parity odd asymmetries for charged pions. Using a
nonlinear sigma model, in QCD these metastable states only appear rather near
the phase transition.Comment: 4 pages, REVTe
Debye screening and Meissner effect in a two-flavor color superconductor
I compute the gluon self-energy in a color superconductor with two flavors of
massless quarks, where condensation of Cooper pairs breaks SU(3)_c to SU(2)_c.
At zero temperature, there is neither Debye screening nor a Meissner effect for
the three gluons of the unbroken SU(2)_c subgroup. The remaining five gluons
attain an electric as well as a magnetic mass. For temperatures approaching the
critical temperature for the onset of color superconductivity, or for gluon
momenta much larger than the color-superconducting gap, the self-energy assumes
the form given by the standard hard-dense loop approximation. The gluon
self-energy determines the coefficient of the kinetic term in the effective
low-energy theory for the condensate fields.Comment: 29 pages, RevTe
Infrared divergence in QED at finite temperature
We consider various ways of treating the infrared divergence which appears in
the dynamically generated fermion mass, when the transverse part of the photon
propagator in N flavour at finite temperature is included in the
Matsubara formalism. This divergence is likely to be an artefact of taking into
account only the leading order term in the expansion when we
calculate the photon propagator and is handled here phenomenologically by means
of an infrared cutoff. Inserting both the longitudinal and the transverse part
of the photon propagator in the Schwinger-Dyson equation we find the dependence
of the dynamically generated fermion mass on the temperature and the cutoff
parameters. It turns out that consistency with certain statistical physics
arguments imposes conditions on the cutoff parameters. For parameters in the
allowed range of values we find that the ratio is approximately 6, consistently with previous calculations which
neglected the transverse photon contribution.Comment: 37 pages, 12 figures, typos corrected, references added, Introduction
rewritte
Lifetime Effects in Color Superconductivity at Weak Coupling
Present computations of the gap of color superconductivity in weak coupling
assume that the quarks which participate in the condensation process are
infinitely long-lived. However, the quasiparticles in a plasma are
characterized by having a finite lifetime. In this article we take into account
this fact to evaluate its effect in the computation of the color gap. By first
considering the Schwinger-Dyson equations in weak coupling, when one-loop
self-energy corrections are included, a general gap equation is written in
terms of the spectral densities of the quasiparticles. To evaluate lifetime
effects, we then model the spectral density by a Lorentzian function. We argue
that the decay of the quasiparticles limits their efficiency to condense. The
value of the gap at the Fermi surface is then reduced. To leading order, these
lifetime effects can be taken into account by replacing the coupling constant
of the gap equation by a reduced effective one.Comment: 16 pages, 2 figures; explanations on the role of the Meissner effect
added; 2 references added; accepted for publication in PR
Hard Thermal Loops and Chiral Lagrangians
Chiral symmetry is used as the guiding principle to derive hard thermal loop
effects in chiral perturbation theory. This is done by using a chiral invariant
background field method for the non-linear sigma model and the
Wess-Zumino-Witten lagrangian, with and without external vector and axial
vector sources. It is then shown that the n-point hard thermal loop is the
leading thermal correction for the Green function of n point vector soft quark
currents.Comment: 15 pages, Revtex, references added, typos corrected, final version to
appear in Phys. Rev.
Anisotropic admixture in color-superconducting quark matter
The analysis of color-superconducting two-flavor deconfined quark matter at
moderate densities is extended to include a particular spin-1 Cooper pairing of
those quarks which do not participate in the standard spin-0 diquark
condensate. (i) The relativistic spin-1 gap Delta' implies spontaneous
breakdown of rotation invariance manifested in the form of the quasi-fermion
dispersion law. (ii) The critical temperature of the anisotropic component is
approximately given by the relation T_c'~ Delta'(T=0)/3. (iii) For massless
fermions the gas of anisotropic Bogolyubov-Valatin quasiquarks becomes
effectively gapless and two-dimensional. Consequently, its specific heat
depends quadratically on temperature. (iv) All collective Nambu-Goldstone
excitations of the anisotropic phase have a linear dispersion law and the whole
system remains a superfluid. (v) The system exhibits an electromagnetic
Meissner effect.Comment: v2: references added, angular dependence of the gap clarified, v3:
extended discussion, typo in eq. (5) corrected, version accepted for
publication in PR
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