1,282 research outputs found
Topological Order and the Quantum Spin Hall Effect
The quantum spin Hall (QSH) phase is a time reversal invariant electronic
state with a bulk electronic band gap that supports the transport of charge and
spin in gapless edge states. We show that this phase is associated with a novel
topological invariant, which distinguishes it from an ordinary insulator.
The classification, which is defined for time reversal invariant
Hamiltonians, is analogous to the Chern number classification of the quantum
Hall effect. We establish the order of the QSH phase in the two band
model of graphene and propose a generalization of the formalism applicable to
multi band and interacting systems.Comment: 4 pages RevTeX. Added reference, minor correction
A path integral derivation of -genus
The formula for the Hirzebruch -genus of complex manifolds is a
consequence of the Hirzebruch-Riemann-Roch formula. The classical index
formulae for Todd genus, Euler number, and Signature correspond to the case
when the complex variable 0, -1, and 1 respectively. Here we give a {\it
direct} derivation of this nice formula based on supersymmetric quantum
mechanics.Comment: 5 page
The Index Theorem and Universality Properties of the Low-lying Eigenvalues of Improved Staggered Quarks
We study various improved staggered quark Dirac operators on quenched gluon
backgrounds in lattice QCD generated using a Symanzik-improved gluon action. We
find a clear separation of the spectrum into would-be zero modes and others.
The number of would-be zero modes depends on the topological charge as expected
from the Index Theorem, and their chirality expectation value is large
(approximately 0.7). The remaining modes have low chirality and show clear
signs of clustering into quartets and approaching the random matrix theory
predictions for all topological charge sectors. We conclude that improvement of
the fermionic and gauge actions moves the staggered quarks closer to the
continuum limit where they respond correctly to QCD topology.Comment: 4 pages, 3 figure
3D N = 1 SYM Chern-Simons theory on the Lattice
We present a method to implement 3-dimensional N = 1 SUSY Yang-Mills theory
(a theory with two real supercharges containing gauge fields and an adjoint
Majorana fermion) on the lattice, including a way to implement the Chern-Simons
term present in this theory. At nonzero Chern-Simons number our implementation
suffers from a sign problem which will make the numerical effort grow
exponentially with volume. We also show that the theory with vanishing
Chern-Simons number is anomalous; its partition function identically vanishes.Comment: v2, minor changes: expanded discussion in section III c, typos
corrected, 17 pages, 9 figure
Equivariance, BRST and Superspace
The structure of equivariant cohomology in non-abelian localization formulas
and topological field theories is discussed. Equivariance is formulated in
terms of a nilpotent BRST symmetry, and another nilpotent operator which
restricts the BRST cohomology onto the equivariant, or basic sector. A
superfield formulation is presented and connections to reducible (BFV)
quantization of topological Yang-Mills theory are discussed.Comment: (24 pages, report UU-ITP and HU-TFT-93-65
The unified Skyrmion profiles and Static Properties of Nucleons
An unified approximated solution for symmetric Skyrmions was proposed for the
SU(2) Skyrme model for baryon numbers up to 8,which take the hybrid form of a
kink-like solution and that given by the instanton method. The Skyrmion
profiles are examined by computing lowest soliton energy as well as the static
properties of nucleons within the framework of collective quantization, with a
good agreement with the exact numeric results. The comparisons with the
previous computations as well as the experimental data are also given.Comment: 6 pages, 3 figures, 3 tables, Created by LaTex Syste
Two-dimensional topological gravity and equivariant cohomology
In this paper, we examine the analogy between topological string theory and
equivariant cohomology. We also show that the equivariant cohomology of a
topological conformal field theory carries a certain algebraic structure, which
we call a gravity algebra. (Error on page 9 corrected: BRS current contains
total derivatives.)Comment: 18 page
Quantum cohomology of flag manifolds and Toda lattices
We discuss relations of Vafa's quantum cohomology with Floer's homology
theory, introduce equivariant quantum cohomology, formulate some conjectures
about its general properties and, on the basis of these conjectures, compute
quantum cohomology algebras of the flag manifolds. The answer turns out to
coincide with the algebra of regular functions on an invariant lagrangian
variety of a Toda lattice.Comment: 35 page
Theory of Anomalous Quantum Hall Effects in Graphene
Recent successes in manufacturing of atomically thin graphite samples
(graphene) have stimulated intense experimental and theoretical activity. The
key feature of graphene is the massless Dirac type of low-energy electron
excitations. This gives rise to a number of unusual physical properties of this
system distinguishing it from conventional two-dimensional metals. One of the
most remarkable properties of graphene is the anomalous quantum Hall effect. It
is extremely sensitive to the structure of the system; in particular, it
clearly distinguishes single- and double-layer samples. In spite of the
impressive experimental progress, the theory of quantum Hall effect in graphene
has not been established. This theory is a subject of the present paper. We
demonstrate that the Landau level structure by itself is not sufficient to
determine the form of the quantum Hall effect. The Hall quantization is due to
Anderson localization which, in graphene, is very peculiar and depends strongly
on the character of disorder. It is only a special symmetry of disorder that
may give rise to anomalous quantum Hall effects in graphene. We analyze the
symmetries of disordered single- and double-layer graphene in magnetic field
and identify the conditions for anomalous Hall quantization.Comment: 13 pages (article + supplementary material), 5 figure
Toric moment mappings and Riemannian structures
Coadjoint orbits for the group SO(6) parametrize Riemannian G-reductions in
six dimensions, and we use this correspondence to interpret symplectic
fibrations between these orbits, and to analyse moment polytopes associated to
the standard Hamiltonian torus action on the coadjoint orbits. The theory is
then applied to describe so-called intrinsic torsion varieties of Riemannian
structures on the Iwasawa manifold.Comment: 25 pages, 14 figures; Geometriae Dedicata 2012, Toric moment mappings
and Riemannian structures, available at
http://www.springerlink.com/content/yn86k22mv18p8ku2
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