2,303 research outputs found
Exact Topological Quantum Order in D=3 and Beyond: Branyons and Brane-Net Condensates
We construct an exactly solvable Hamiltonian acting on a 3-dimensional
lattice of spin- systems that exhibits topological quantum order.
The ground state is a string-net and a membrane-net condensate. Excitations
appear in the form of quasiparticles and fluxes, as the boundaries of strings
and membranes, respectively. The degeneracy of the ground state depends upon
the homology of the 3-manifold. We generalize the system to , were
different topological phases may occur. The whole construction is based on
certain special complexes that we call colexes.Comment: Revtex4 file, color figures, minor correction
Entanglement, fidelity and topological entropy in a quantum phase transition to topological order
We present a numerical study of a quantum phase transition from a
spin-polarized to a topologically ordered phase in a system of spin-1/2
particles on a torus. We demonstrate that this non-symmetry-breaking
topological quantum phase transition (TOQPT) is of second order. The transition
is analyzed via the ground state energy and fidelity, block entanglement,
Wilson loops, and the recently proposed topological entropy. Only the
topological entropy distinguishes the TOQPT from a standard QPT, and
remarkably, does so already for small system sizes. Thus the topological
entropy serves as a proper order parameter. We demonstrate that our conclusions
are robust under the addition of random perturbations, not only in the
topological phase, but also in the spin polarized phase and even at the
critical point.Comment: replaced with published versio
Fermion localization on degenerate and critical branes
In this work we analyze the localization of fermions on degenerate and
critical Bloch branes. This is done directly on physical coordinates, in
constrast to some works that has been using conformal coordinates. We find the
range of coupling constants of the interaction of fermions with the scalar
fields that allow us to have normalizable fermion zero-mode localized on the
brane on both, critical and degenerate Bloch branes. In the case of critical
branes our results agree with those found in [Class. Quantum Grav. \textbf{27}
(2010) 185001]. The results on fermion localization on degenerate Bloch branes
are new. We also propose a coupling of fermions to the scalar fields which
leads to localization of massless fermion on both sides of a double-brane.Comment: 16 pages, 6 figure
Framework for classifying logical operators in stabilizer codes
Entanglement, as studied in quantum information science, and non-local
quantum correlations, as studied in condensed matter physics, are fundamentally
akin to each other. However, their relationship is often hard to quantify due
to the lack of a general approach to study both on the same footing. In
particular, while entanglement and non-local correlations are properties of
states, both arise from symmetries of global operators that commute with the
system Hamiltonian. Here, we introduce a framework for completely classifying
the local and non-local properties of all such global operators, given the
Hamiltonian and a bi-partitioning of the system. This framework is limited to
descriptions based on stabilizer quantum codes, but may be generalized. We
illustrate the use of this framework to study entanglement and non-local
correlations by analyzing global symmetries in topological order, distribution
of entanglement and entanglement entropy.Comment: 20 pages, 9 figure
Hamiltonian lattice QCD at finite chemical potential
At sufficiently high temperature and density, quantum chromodynamics (QCD) is
expected to undergo a phase transition from the confined phase to the
quark-gluon plasma phase. In the Lagrangian lattice formulation the Monte Carlo
method works well for QCD at finite temperature, however, it breaks down at
finite chemical potential. We develop a Hamiltonian approach to lattice QCD at
finite chemical potential and solve it in the case of free quarks and in the
strong coupling limit. At zero temperature, we calculate the vacuum energy,
chiral condensate, quark number density and its susceptibility, as well as mass
of the pseudoscalar, vector mesons and nucleon. We find that the chiral phase
transition is of first order, and the critical chemical potential is (dynamical quark mass at ). This is consistent with
(where is the nucleon mass at ).Comment: Final version appeared in Phys. Rev.
Twisted and Nontwisted Bifurcations Induced by Diffusion
We discuss a diffusively perturbed predator-prey system. Freedman and
Wolkowicz showed that the corresponding ODE can have a periodic solution that
bifurcates from a homoclinic loop. When the diffusion coefficients are large,
this solution represents a stable, spatially homogeneous time-periodic solution
of the PDE. We show that when the diffusion coefficients become small, the
spatially homogeneous periodic solution becomes unstable and bifurcates into
spatially nonhomogeneous periodic solutions.
The nature of the bifurcation is determined by the twistedness of an
equilibrium/homoclinic bifurcation that occurs as the diffusion coefficients
decrease. In the nontwisted case two spatially nonhomogeneous simple periodic
solutions of equal period are generated, while in the twisted case a unique
spatially nonhomogeneous double periodic solution is generated through
period-doubling.
Key Words: Reaction-diffusion equations; predator-prey systems; homoclinic
bifurcations; periodic solutions.Comment: 42 pages in a tar.gz file. Use ``latex2e twisted.tex'' on the tex
files. Hard copy of figures available on request from
[email protected]
Positivity Constraints on Anomalies in Supersymmetric Gauge Theories
The relation between the trace and R-current anomalies in supersymmetric
theories implies that the U, U and U anomalies which
are matched in studies of N=1 Seiberg duality satisfy positivity constraints.
Some constraints are rigorous and others conjectured as four-dimensional
generalizations of the Zamolodchikov -theorem. These constraints are tested
in a large number of N=1 supersymmetric gauge theories in the non-Abelian
Coulomb phase, and they are satisfied in all renormalizable models with unique
anomaly-free R-current, including those with accidental symmetry. Most striking
is the fact that the flow of the Euler anomaly coefficient, , is
always positive, as conjectured by Cardy.Comment: latex, 36 page
Maxwell-Chern-Simons Theory With Boundary
The Maxwell-Chern-Simons (MCS) theory with planar boundary is considered. The
boundary is introduced according to Symanzik's basic principles of locality and
separability. A method of investigation is proposed, which, avoiding the
straight computation of correlators, is appealing for situations where the
computation of propagators, modified by the boundary, becomes quite complex.
For MCS theory, the outcome is that a unique solution exists, in the form of
chiral conserved currents, satisfying a Kac-Moody algebra, whose central charge
does not depend on the Maxwell term.Comment: 30 page
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