3,778 research outputs found
The transition temperature of the dilute interacting Bose gas for internal degrees of freedom
We calculate explicitly the variation of the Bose-Einstein
condensation temperature induced by weak repulsive two-body interactions
to leading order in the interaction strength. As shown earlier by general
arguments, is linear in the dimensionless product
to leading order, where is the density and the scattering length. This
result is non-perturbative, and a direct perturbative calculation of the
amplitude is impossible due to infrared divergences familiar from the study of
the superfluid helium lambda transition. Therefore we introduce here another
standard expansion scheme, generalizing the initial model which depends on one
complex field to one depending on real fields, and calculating the
temperature shift at leading order for large . The result is explicit and
finite. The reliability of the result depends on the relevance of the large
expansion to the situation N=2, which can in principle be checked by systematic
higher order calculations. The large result agrees remarkably well with
recent numerical simulations.Comment: 10 pages, Revtex, submitted to Europhysics Letter
A renormalized large-n solution of the U(n) x U(n) linear sigma model in the broken symmetry phase
Dyson-Schwinger equations for the U(n) x U(n) symmetric matrix sigma model
reformulated with two auxiliary fields in a background breaking the symmetry to
U(n) are studied in the so-called bare vertex approximation. A large n solution
is constructed under the supplementary assumption so that the scalar components
are much heavier than the pseudoscalars. The renormalizability of the solution
is investigated by explicit construction of the counterterms.Comment: RevTeX4, 14 pages, 2 figures. Version published in Phys. Rev.
Condensation temperature of interacting Bose gases with and without disorder
The momentum-shell renormalization group (RG) is used to study the
condensation of interacting Bose gases without and with disorder. First of all,
for the homogeneous disorder-free Bose gas the interaction-induced shifts in
the critical temperature and chemical potential are determined up to second
order in the scattering length. The approach does not make use of dimensional
reduction and is thus independent of previous derivations. Secondly, the RG is
used together with the replica method to study the interacting Bose gas with
delta-correlated disorder. The flow equations are derived and found to reduce,
in the high-temperature limit, to the RG equations of the classical
Landau-Ginzburg model with random-exchange defects. The random fixed point is
used to calculate the condensation temperature under the combined influence of
particle interactions and disorder.Comment: 7 pages, 2 figure
Nonperturbative Functional Renormalization Group for Random Field Models. III: Superfield formalism and ground-state dominance
We reformulate the nonperturbative functional renormalization group for the
random field Ising model in a superfield formalism, extending the
supersymmetric description of the critical behavior of the system first
proposed by Parisi and Sourlas [Phys. Rev. Lett. 43, 744 (1979)]. We show that
the two crucial ingredients for this extension are the introduction of a
weighting factor, which accounts for ground-state dominance when multiple
metastable states are present, and of multiple copies of the original system,
which allows one to access the full functional dependence of the cumulants of
the renormalized disorder and to describe rare events. We then derive exact
renormalization group equations for the flow of the renormalized cumulants
associated with the effective average action.Comment: 28 page
Disorder-induced metal-insulator transitions in three-dimensional topological insulators and superconductors
We discuss the effects of disorder in time-reversal invariant topological
insulators and superconductors in three spatial dimensions. For
three-dimensional topological insulator in symplectic (AII) symmetry class, the
phase diagram in the presence of disorder and a mass term, which drives a
transition between trivial and topological insulator phases, is computed
numerically by the transfer matrix method. The numerics is supplemented by a
field theory analysis (the large- expansion where is the number of
valleys or Dirac cones), from which we obtain the correlation length exponent,
and several anomalous dimensions at a non-trivial critical point separating a
metallic phase and a Dirac semi-metal. A similar field theory approach is
developed for disorder-driven transitions in symmetry class AIII, CI, and DIII.
For these three symmetry classes, where topological superconductors are
characterized by integer topological invariant, a complementary description is
given in terms of the non-linear sigma model supplemented with a topological
term which is a three-dimensional analogue of the Pruisken term in the integer
quantum Hall effect.Comment: 19 pages, 5 figure
Superfluidity and magnetism in multicomponent ultracold fermions
We study the interplay between superfluidity and magnetism in a
multicomponent gas of ultracold fermions. Ward-Takahashi identities constrain
possible mean-field states describing order parameters for both pairing and
magnetization. The structure of global phase diagrams arises from competition
among these states as functions of anisotropies in chemical potential, density,
or interactions. They exhibit first and second order phase transition as well
as multicritical points, metastability regions, and phase separation. We
comment on experimental signatures in ultracold atoms.Comment: 4 pages, 3 figure
Seiberg-Witten maps and noncommutative Yang-Mills theories for arbitrary gauge groups
Seiberg-Witten maps and a recently proposed construction of noncommutative
Yang-Mills theories (with matter fields) for arbitrary gauge groups are
reformulated so that their existence to all orders is manifest. The ambiguities
of the construction which originate from the freedom in the Seiberg-Witten map
are discussed with regard to the question whether they can lead to inequivalent
models, i.e., models not related by field redefinitions.Comment: 12 pages; references added, minor misprints correcte
Background gauge invariance in the antifield formalism for theories with open gauge algebras
We show that any BRST invariant quantum action with open or closed gauge
algebra has a corresponding local background gauge invariance. If the BRST
symmetry is anomalous, but the anomaly can be removed in the antifield
formalism, then the effective action possesses a local background gauge
invariance. The presence of antifields (BRST sources) is necessary. As an
example we analyze chiral gravity.Comment: 17pp., Latex, mispelling in my name! corrected, no other change
Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
We study the effect of hedgehog suppression in the O(3) sigma model in D=2+1.
We show via Monte Carlo simulations that the sigma model can be disordered
while effectively forbidding these point topological defects. The resulting
paramagnetic state has gauge charged matter with half-integer spin (spinons)
and also an emergent gauge field (photons), whose existence is explicitly
demonstrated. Hence, this is an explicit realization of fractionalization in a
model with global SU(2) symmetry. The zero temperature ordering transition from
this phase is found to be continuous but distinct from the regular Heisenberg
ordering transition. We propose that these phases and this phase transition are
captured by the {\it noncompact} model, which contains a pair of bosonic
fields coupled to a noncompact U(1) gauge field. Direct simulation of the
transition in this model yields critical exponents that support this claim. The
easy-plane limit of this model also displays a continuous zero temperature
ordering transition, which has the remarkable property of being self-dual. The
presence of emergent gauge charge and hence Coulomb interactions is evidenced
by the presence of a finite temperature Kosterlitz-Thouless transition
associated with the thermal ionization of the gauge charged spinons.
Generalization to higher dimensions and the effects of nonzero hedgehog
fugacity are discussed.Comment: 13 pages, 8 figures. Phase boundaries in fig7 corrected, reference
added. To appear in Phys. Rev.
Temperature driven structural phase transition for trapped ions and its experimental detection
A Wigner crystal formed with trapped ion can undergo structural phase
transition, which is determined only by the mechanical conditions on a
classical level. Instead of this classical result, we show that through
consideration of quantum and thermal fluctuation, a structural phase transition
can be solely driven by change of the system's temperature. We determine a
finite-temperature phase diagram for trapped ions using the renormalization
group method and the path integral formalism, and propose an experimental
scheme to observe the predicted temperature-driven structural phase transition,
which is well within the reach of the current ion trap technology.Comment: 4 pages, 5 figure
- …