21,413 research outputs found
Symmetry-protected many-body Aharonov-Bohm effect
It is known as a purely quantum effect that a magnetic flux affects the real
physics of a particle, such as the energy spectrum, even if the flux does not
interfere with the particle's path - the Aharonov-Bohm effect. Here we examine
an Aharonov-Bohm effect on a many-body wavefunction. Specifically, we study
this many-body effect on the gapless edge states of a bulk gapped phase
protected by a global symmetry (such as ) - the
symmetry-protected topological (SPT) states. The many-body analogue of spectral
shifts, the twisted wavefunction and the twisted boundary realization are
identified in this SPT state. An explicit lattice construction of SPT edge
states is derived, and a challenge of gauging its non-onsite symmetry is
overcome. Agreement is found in the twisted spectrum between a numerical
lattice calculation and a conformal field theory prediction.Comment: 5 pages main text + 8 pages appendix, 3 figures. v2: nearly PRB
versio
Topological superconductors as nonrelativistic limits of Jackiw-Rossi and Jackiw-Rebbi models
We argue that the nonrelativistic Hamiltonian of p_x+ip_y superconductor in
two dimensions can be derived from the relativistic Jackiw-Rossi model by
taking the limit of large Zeeman magnetic field and chemical potential. In
particular, the existence of a fermion zero mode bound to a vortex in the
p_x+ip_y superconductor can be understood as a remnant of that in the
Jackiw-Rossi model. In three dimensions, the nonrelativistic limit of the
Jackiw-Rebbi model leads to a "p+is" superconductor in which spin-triplet
p-wave and spin-singlet s-wave pairings coexist. The resulting Hamiltonian
supports a fermion zero mode when the pairing gaps form a hedgehoglike
structure. Our findings provide a unified view of fermion zero modes in
relativistic (Dirac-type) and nonrelativistic (Schr\"odinger-type)
superconductors.Comment: 7 pages, no figure; published versio
Isolated Flat Bands and Spin-1 Conical Bands in Two-Dimensional Lattices
Dispersionless bands, such as Landau levels, serve as a good starting point
for obtaining interesting correlated states when interactions are added. With
this motivation in mind, we study a variety of dispersionless ("flat") band
structures that arise in tight-binding Hamiltonians defined on hexagonal and
kagome lattices with staggered fluxes. The flat bands and their neighboring
dispersing bands have several notable features: (a) Flat bands can be isolated
from other bands by breaking time reversal symmetry, allowing for an extensive
degeneracy when these bands are partially filled; (b) An isolated flat band
corresponds to a critical point between regimes where the band is electron-like
or hole-like, with an anomalous Hall conductance that changes sign across the
transition; (c) When the gap between a flat band and two neighboring bands
closes, the system is described by a single spin-1 conical-like spectrum,
extending to higher angular momentum the spin-1/2 Dirac-like spectra in
topological insulators and graphene; and (d) some configurations of parameters
admit two isolated parallel flat bands, raising the possibility of exotic
"heavy excitons"; (e) We find that the Chern number of the flat bands, in all
instances that we study here, is zero.Comment: 7 pages. Sec. II slightly expanded. References adde
Open String Descriptions of Space-like Singularities in Two Dimensional String Theory
The matrix model formulation of two dimensional string theory has been shown
to admit time dependent classical solutions whose closed string duals are
geodesically incomplete space-times with space-like boundaries. We investigate
some aspects of the dynamics of fermions in one such background. We show that
even though the background solution appears pathological, the time evolution of
the system is smooth in terms of open string degrees of freedom, viz. the
fermions. In particular, an initial state of fermions evolves smoothly into a
well defined final state over an infinite open string time interval, while the
time perceived by closed strings appears to end abruptly. We outline a method
of calculating fermion correlators exactly using symmetry properties. The
result for the two point function is consistent with the semiclassical picture.Comment: LaTeX 8 eps figures, referenced adde
Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
The properties of the isotropic incompressible fractional quantum
Hall (FQH) state are described by a paired state of composite fermions in zero
(effective) magnetic field, with a uniform pairing order parameter,
which is a non-Abelian topological phase with chiral Majorana and charge modes
at the boundary. Recent experiments suggest the existence of a proximate
nematic phase at . This finding motivates us to consider an
inhomogeneous paired state - a pair-density-wave (PDW) - whose
melting could be the origin of the observed liquid-crystalline phases. This
state can viewed as an array of domain and anti-domain walls of the
order parameter. We show that the nodes of the PDW order parameter, the
location of the domain walls (and anti-domain walls) where the order parameter
changes sign, support a pair of symmetry-protected counter-propagating Majorana
modes. The coupling behavior of the domain wall Majorana modes crucially
depends on the interplay of the Fermi energy and the PDW pairing energy
. The analysis of this interplay yields a rich set of
topological states. The pair-density-wave order state in paired FQH system
provides a fertile setting to study Abelian and non-Abelian FQH phases - as
well as transitions thereof - tuned by the strength of the paired liquid
crystalline order.Comment: 27 pages, 11 figures; Published versio
Bosonic Anomalies, Induced Fractional Quantum Numbers and Degenerate Zero Modes: the anomalous edge physics of Symmetry-Protected Topological States
The boundary of symmetry-protected topological states (SPTs) can harbor new
quantum anomaly phenomena. In this work, we characterize the bosonic anomalies
introduced by the 1+1D non-onsite-symmetric gapless edge modes of 2+1D bulk
bosonic SPTs with a generic finite Abelian group symmetry (isomorphic to
). We
demonstrate that some classes of SPTs (termed "Type II") trap fractional
quantum numbers (such as fractional charges) at the 0D kink of the
symmetry-breaking domain walls; while some classes of SPTs (termed "Type III")
have degenerate zero energy modes (carrying the projective representation
protected by the unbroken part of the symmetry), either near the 0D kink of a
symmetry-breaking domain wall, or on a symmetry-preserving 1D system
dimensionally reduced from a thin 2D tube with a monodromy defect 1D line
embedded. More generally, the energy spectrum and conformal dimensions of
gapless edge modes under an external gauge flux insertion (or twisted by a
branch cut, i.e., a monodromy defect line) through the 1D ring can distinguish
many SPT classes. We provide a manifest correspondence from the physical
phenomena, the induced fractional quantum number and the zero energy mode
degeneracy, to the mathematical concept of cocycles that appears in the group
cohomology classification of SPTs, thus achieving a concrete physical
materialization of the cocycles. The aforementioned edge properties are
formulated in terms of a long wavelength continuum field theory involving
scalar chiral bosons, as well as in terms of Matrix Product Operators and
discrete quantum lattice models. Our lattice approach yields a regularization
with anomalous non-onsite symmetry for the field theory description. We also
formulate some bosonic anomalies in terms of the Goldstone-Wilczek formula.Comment: 29 pages, 12 Figures. v3 clarification to be accessible for both HEP
and CMT. Thanks to Roman Jackiw for introducing new Ref
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