15 research outputs found
Chiral Dynamics and Fermion Mass Generation in Three Dimensional Gauge Theory
We examine the possibility of fermion mass generation in 2+1- dimensional
gauge theory from the current algebra point of view.In our approach the
critical behavior is governed by the fluctuations of pions which are the
Goldstone bosons for chiral symmetry breaking. Our analysis supports the
existence of an upper critical number of Fermion flavors and exhibits the
explicit form of the gap equation as well as the form of the critical exponent
for the inverse correlation lenght of the order parameterComment: Latex,10 pages,DFUPG 70/9
Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point
We study the adiabatic dynamics of Majorana fermions across a quantum phase
transition. We show that the Kibble-Zurek scaling, which describes the density
of bulk defects produced during the critical point crossing, is not valid for
edge Majorana fermions. Therefore, the dynamics governing an edge state quench
is nonuniversal and depends on the topological features of the system. Besides,
we show that the localization of Majorana fermions is a necessary ingredient to
guaranty robustness against defect production.Comment: Submitted to the Special Issue on "Dynamics and Thermalization in
Isolated Quantum Many-Body Systems" in New Journal of Physics. Editors:M.
Cazalilla, M. Rigol. New references and some typos correcte
Oblique Confinement and Phase Transitions in Chern-Simons Gauge Theories
We investigate non-perturbative features of a planar Chern-Simons gauge
theory modeling the long distance physics of quantum Hall systems, including a
finite gap M for excitations. By formulating the model on a lattice, we
identify the relevant topological configurations and their interactions. For M
bigger than a critical value, the model exhibits an oblique confinement phase,
which we identify with Lauglin's incompressible quantum fluid. For M smaller
than the critical value, we obtain a phase transition to a Coulomb phase or a
confinement phase, depending on the value of the electromagnetic coupling.Comment: 8 pages, harvmac, DFUPG 91/94 and MPI-PhT/94-9
Chiral Symmetry Breaking on the Lattice: a Study of the Strongly Coupled Lattice Schwinger Model
We revisit the strong coupling limit of the Schwinger model on the lattice
using staggered fermions and the hamiltonian approach to lattice gauge
theories. Although staggered fermions have no continuous chiral symmetry, they
posses a discrete axial invari ance which forbids fermion mass and which must
be broken in order for the lattice Schwinger model to exhibit the features of
the spectrum of the continuum theory. We show that this discrete symmetry is
indeed broken spontaneously in the strong coupling li mit. Expanding around a
gauge invariant ground state and carefully considering the normal ordering of
the charge operator, we derive an improved strong coupling expansion and
compute the masses of the low lying bosonic excitations as well as the chiral
co ndensate of the model. We find very good agreement between our lattice
calculations and known continuum values for these quantities already in the
fourth order of strong coupling perturbation theory. We also find the exact
ground state of the antiferromag netic Ising spin chain with long range Coulomb
interaction, which determines the nature of the ground state in the strong
coupling limit.Comment: 24 pages, Latex, no figure
Confinement-Deconfinement Transition in 3-Dimensional QED
We argue that, at finite temperature, parity invariant non-compact
electrodynamics with massive electrons in 2+1 dimensions can exist in both
confined and deconfined phases. We show that an order parameter for the
confinement-deconfinement phase transition is the Polyakov loop operator whose
average measures the free energy of a test charge that is not an integral
multiple of the electron charge. The effective field theory for the Polyakov
loop operator is a 2-dimensional Euclidean scalar field theory with a global
discrete symmetry , the additive group of the integers. We argue that the
realization of this symmetry governs confinement and that the
confinement-deconfinement phase transition is of
Berezinskii-Kosterlitz-Thouless type. We compute the effective action to
one-loop order and argue that when the electron mass is much greater than
the temperature and dimensional coupling , the effective field theory
is the Sine-Gordon model. In this limit, we estimate the critical temperature,
.Comment: 11 pages, latex, no figure
The Strongly Coupled 't Hooft Model on the Lattice
We study the strong coupling limit of the one-flavor and two-flavor massless
't Hooft models, -color , on a lattice. We use
staggered fermions and the Hamiltonian approach to lattice gauge theories. We
show that the one-flavor model is effectively described by the
antiferromagnetic Ising model, whose ground state is the vacuum of the gauge
model in the infinite coupling limit; expanding around this ground state we
derive a strong coupling expansion and compute the lowest lying hadron masses
as well as the chiral condensate of the gauge theory. Our lattice computation
well reproduces the results of the continuum theory. Baryons are massless in
the infinite coupling limit; they acquire a mass already at the second order in
the strong coupling expansion in agreement with the Witten argument that
baryons are the solitons.
The spectrum and chiral condensate of the two-flavor model are effectively
described in terms of observables of the quantum antiferromagnetic Heisenberg
model. We explicitly write the lowest lying hadron masses and chiral condensate
in terms of spin-spin correlators on the ground state of the spin model. We
show that the planar limit () of the gauge
model corresponds to the large spin limit () of the
antiferromagnet and compute the hadron mass spectrum in this limit finding
that, also in this model, the pattern of chiral symmetry breaking of the
continuum theory is well reproduced on the lattice.Comment: LaTex, 25 pages, no figure