793 research outputs found
Phase-diagram of two-color lattice QCD in the chiral limit
We study thermodynamics of strongly coupled lattice QCD with two colors of
massless staggered fermions as a function of the baryon chemical potential
in 3+1 dimensions using a new cluster algorithm. We find evidence that
the model undergoes a weak first order phase transition at which
becomes second order at a finite . Symmetry considerations suggest that
the universality class of these phase transitions should be governed by an
field theory with collinear order, with N=3 at and
N=2 at . The universality class of the second order phase
transition at appears to be governed by the decoupled XY fixed
point present in the field theory. Finally we show that the
quantum (T=0) phase transition as a function of is a second order mean
field transition.Comment: 31 pages, 12 figure
Chiral Limit of Strongly Coupled Lattice Gauge Theories
We construct a new and efficient cluster algorithm for updating strongly
coupled U(N) lattice gauge theories with staggered fermions in the chiral
limit. The algorithm uses the constrained monomer-dimer representation of the
theory and should also be of interest to researchers working on other models
with similar constraints. Using the new algorithm we address questions related
to the chiral limit of strongly coupled U(N) gauge theories beyond the mean
field approximation. We show that the infinite volume chiral condensate is
non-zero in three and four dimensions. However, on a square lattice of size
we find for large
where . These results differ from an
earlier conclusion obtained using a different algorithm. Here we argue that the
earlier calculations were misleading due to uncontrolled autocorrelation times
encountered by the previous algorithm.Comment: 36 Pages, 9 figures, aps revtex forma
Topological Phases in Neuberger-Dirac operator
The response of the Neuberger-Dirac fermion operator D=\Id + V in the
topologically nontrivial background gauge field depends on the negative mass
parameter in the Wilson-Dirac fermion operator which enters
through the unitary operator . We classify
the topological phases of by comparing its index to the topological charge
of the smooth background gauge field. An exact discrete symmetry in the
topological phase diagram is proved for any gauge configurations. A formula for
the index of D in each topological phase is derived by obtaining the total
chiral charge of the zero modes in the exact solution of the free fermion
propagator.Comment: 27 pages, Latex, 3 figures, appendix A has been revise
Ground State and Excitations of Quantum Dots with "Magnetic Impurities"
We consider an "impurity" with a spin degree of freedom coupled to a finite
reservoir of non-interacting electrons, a system which may be realized by
either a true impurity in a metallic nano-particle or a small quantum dot
coupled to a large one. We show how the physics of such a spin impurity is
revealed in the many-body spectrum of the entire finite-size system; in
particular, the evolution of the spectrum with the strength of the
impurity-reservoir coupling reflects the fundamental many-body correlations
present. Explicit calculation in the strong and weak coupling limits shows that
the spectrum and its evolution are sensitive to the nature of the impurity and
the parity of electrons in the reservoir. The effect of the finite size
spectrum on two experimental observables is considered. First, we propose an
experimental setup in which the spectrum may be conveniently measured using
tunneling spectroscopy. A rate equation calculation of the differential
conductance suggests how the many-body spectral features may be observed.
Second, the finite-temperature magnetic susceptibility is presented, both the
impurity susceptibility and the local susceptibility. Extensive quantum
Monte-Carlo calculations show that the local susceptibility deviates from its
bulk scaling form. Nevertheless, for special assumptions about the reservoir --
the "clean Kondo box" model -- we demonstrate that finite-size scaling is
recovered. Explicit numerical evaluations of these scaling functions are given,
both for even and odd parity and for the canonical and grand-canonical
ensembles.Comment: 16 pages; published version, corrections to figure and equation,
clarification
Kosterlitz-Thouless Universality in a Fermionic System
A new extension of the attractive Hubbard model is constructed to study the
critical behavior near a finite temperature superconducting phase transition in
two dimensions using the recently developed meron-cluster algorithm. Unlike
previous calculations in the attractive Hubbard model which were limited to
small lattices, the new algorithm is used to study the critical behavior on
lattices as large as . These precise results for the first time
show that a fermionic system can undergo a finite temperature phase transition
whose critical behavior is well described by the predictions of Kosterlitz and
Thouless almost three decades ago. In particular it is confirmed that the
spatial winding number susceptibility obeys the well known predictions of
finite size scaling for and up to logarithmic corrections the pair
susceptibility scales as at large volumes with for .Comment: Revtex format; 4 pages, 2 figure
Role of the -resonance in determining the convergence of chiral perturbation theory
The dimensionless parameter , where
is the pion decay constant and is the pion mass, is expected to control
the convergence of chiral perturbation theory applicable to QCD. Here we
demonstrate that a strongly coupled lattice gauge theory model with the same
symmetries as two-flavor QCD but with a much lighter -resonance is
different. Our model allows us to study efficiently the convergence of chiral
perturbation theory as a function of . We first confirm that the leading
low energy constants appearing in the chiral Lagrangian are the same when
calculated from the -regime and the -regime as expected. However,
is necessary before 1-loop chiral perturbation theory
predicts the data within 1%. For the data begin to deviate
dramatically from 1-loop chiral perturbation theory predictions. We argue that
this qualitative change is due to the presence of a light -resonance in
our model. Our findings may be useful for lattice QCD studies.Comment: 5 pages, 6 figures, revtex forma
Anomalous Chiral Symmetry Breaking above the QCD Phase Transition
We study the anomalous breaking of U_A(1) symmetry just above the QCD phase
transition for zero and two flavors of quarks, using a staggered fermion,
lattice discretization. The properties of the QCD phase transition are expected
to depend on the degree of U_A(1) symmetry breaking in the transition region.
For the physical case of two flavors, we carry out extensive simulations on a
16^3 x 4 lattice, measuring a difference in susceptibilities which is sensitive
to U_A(1) symmetry and which avoids many of the staggered fermion
discretization difficulties. The results suggest that anomalous effects are at
or below the 15% level.Comment: 10 pages including 2 figures and 1 tabl
Dirac eigenvalues and eigenvectors at finite temperature
We investigate the eigenvalues and eigenvectors of the staggered Dirac
operator in the vicinity of the chiral phase transition of quenched SU(3)
lattice gauge theory. We consider both the global features of the spectrum and
the local correlations. In the chirally symmetric phase, the local correlations
in the bulk of the spectrum are still described by random matrix theory, and we
investigate the dependence of the bulk Thouless energy on the simulation
parameters. At and above the critical point, the properties of the low-lying
Dirac eigenvalues depend on the -phase of the Polyakov loop. In the real
phase, they are no longer described by chiral random matrix theory. We also
investigate the localization properties of the Dirac eigenvectors in the
different -phases.Comment: Lattice 2000 (Finite Temperature), 5 page
Constraints and Period Relations in Bosonic Strings at Genus-g
We examine some of the implications of implementing the usual boundary
conditions on the closed bosonic string in the hamiltonian framework. Using the
KN formalism, it is shown that at the quantum level, the resulting constraints
lead to relations among the periods of the basis 1-forms. These are compared
with those of Riemanns' which arise from a different consideration.Comment: 16 pages, (Plain Tex), NUS/HEP/9320
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