15,821 research outputs found
Gapless Fermions and Quantum Order
Using 2D quantum spin-1/2 model as a concrete example, we studied the
relation between gapless fermionic excitations (spinons) and quantum orders in
some spin liquid states. Using winding number, we find the projective symmetry
group that characterizes the quantum order directly determines the pattern of
Fermi points in the Brillouin zone. Thus quantum orders provide an origin for
gapless fermionic excitations.Comment: 23 pages. LaTeX. Homepage http://dao.mit.edu/~we
Continuous topological phase transitions between clean quantum Hall states
Continuous transitions between states with the {\em same} symmetry but
different topological orders are studied. Clean quantum Hall (QH) liquids with
neutral quasiparticles are shown to have such transitions. For clean bilayer
(nnm) states, a continous transition to other QH states (including non-Abelian
states) can be driven by increasing interlayer repulsion/tunneling. The
effective theories describing the critical points at some transitions are
derived.Comment: 4 pages, RevTeX, 2 eps figure
Tunable waveguide lattices with non-uniform parity-symmetric tunneling
We investigate the single-particle time evolution and two-particle quantum
correlations in a one-dimensional -site lattice with a site-dependent
nearest neighbor tunneling function . Since
the bandwidth and the energy levels spacings for such a lattice both depend
upon , we show that the observable properties of a wavepacket, such as
its spread and the relative phases of its constitutents, vary dramatically as
is varied from positive to negative values. We also find that the
quantum correlations are exquisitely sensitive to the form of the tunneling
function. Our results suggest that arrays of waveguides with position-dependent
evanascent couplings will show rich dynamics with no counterpart in
present-day, traditional systems.Comment: 5 pages, 4 figure
Binding Transition in Quantum Hall Edge States
We study a class of Abelian quantum Hall (QH) states which are topologically
unstable (T-unstable). We find that the T-unstable QH states can have a phase
transition on the edge which causes a binding between electrons and reduces the
number of gapless edge branches. After the binding transition, the
single-electron tunneling into the edge gains a finite energy gap, and only
certain multi-electron co-tunneling (such as three-electron co-tunneling for
edges) can be gapless. Similar phenomenon also appear for edge state
on the boundary between certain QH states. For example edge on the boundary
between and states only allow three-electron co-tunneling at
low energies after the binding transition.Comment: 4 pages, RevTeX, 1 figur
The Grassmannian Sigma Model in SU(2) Yang-Mills Theory
Spin-charge separation in pure SU(2) Yang-Mills theory was recently found to
involve the dynamics of an O(3) non-linear sigma model and, seemingly, a
Grassmannian non-linear sigma model. In this article we explicitly construct
the Grassmannian sigma model of the form appearing in the the spin-charge
separated SU(2) theory through a quaternionic decomposition of the manifold,
thus verifying its relevance in this context. The coupling between this model
and the O(3) non-linear sigma model is further commented upon.Comment: 11 pages, undergraduate research project; version published in J.
Phys.
Robust and fragile PT-symmetric phases in a tight-binding chain
We study the phase-diagram of a parity and time-reversal (PT) symmetric
tight-binding chain with sites and hopping energy , in the presence of
two impurities with imaginary potentials located at arbitrary
(P-symmetric) positions on the chain where . We
find that except in the two special cases where impurities are either the
farthest or the closest, the PT-symmetric region - defined as the region in
which all energy eigenvalues are real - is algebraically fragile. We
analytically and numerically obtain the critical impurity potential
and show that as
except in the two special cases. When the PT symmetry is
spontaneously broken, we find that the maximum number of complex eigenvalues is
given by . When the two impurities are the closest, we show that the
critical impurity strength in the limit
approaches () provided that is even (odd). For an even the PT
symmetry is maximally broken whereas for an odd , it is sequentially broken.
Our results show that the phase-diagram of a PT-symmetric tight-binding chain
is extremely rich and that, in the continuum limit, this model may give rise to
new PT-symmetric Hamiltonians.Comment: 10 pages, 4 figure
Angular Momentum Distribution Function of the Laughlin Droplet
We have evaluated the angular-momentum distribution functions for finite
numbers of electrons in Laughlin states. For very small numbers of electrons
the angular-momentum state occupation numbers have been evaluated exactly while
for larger numbers of electrons they have been obtained from Monte-Carlo
estimates of the one-particle density matrix. An exact relationship, valid for
any number of electrons, has been derived for the ratio of the occupation
numbers of the two outermost orbitals of the Laughlin droplet and is used to
test the accuracy of the MC calculations. We compare the occupation numbers
near the outer edges of the droplets with predictions based on the chiral
Luttinger liquid picture of Laughlin state edges and discuss the surprisingly
large oscillations in occupation numbers which occur for angular momenta far
from the edge.Comment: 11 pages of RevTeX, 2 figures available on request. IUCM93-00
Thermodynamics with density and temperature dependent particle masses and properties of bulk strange quark matter and strangelets
Thermodynamic formulas for investigating systems with density and/or
temperature dependent particle masses are generally derived from the
fundamental derivation equality of thermodynamics. Various problems in the
previous treatments are discussed and modified. Properties of strange quark
matter in bulk and strangelets at both zero and finite temperature are then
calculated based on the new thermodynamic formulas with a new quark mass
scaling, which indicates that low mass strangelets near beta equilibrium are
multi-quark states with an anti-strange quark, such as the pentaquark
(u^2d^2\bar{s}) for baryon nmber 1 and the octaquark (u^4d^3\bar{s}) for
dibaryon etc.Comment: 14 pages, 12 figures, Revtex4 styl
Fractional Quantum Hall Effect in Topological Flat Bands with Chern Number Two
Recent theoretical works have demonstrated various robust Abelian and
non-Abelian fractional topological phases in lattice models with topological
flat bands carrying Chern number C=1. Here we study hard-core bosons and
interacting fermions in a three-band triangular-lattice model with the lowest
topological flat band of Chern number C=2. We find convincing numerical
evidence of bosonic fractional quantum Hall effect at the filling
characterized by three-fold quasi-degeneracy of ground states on a torus, a
fractional Chern number for each ground state, a robust spectrum gap, and a gap
in quasihole excitation spectrum. We also observe numerical evidence of a
robust fermionic fractional quantum Hall effect for spinless fermions at the
filling with short-range interactions.Comment: 5 pages, 7 figures, with Supplementary Materia
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