20 research outputs found
Spectroscopic signatures of crystal momentum fractionalization
We consider gapped Z2 spin liquids, where spinon quasiparticles may carry
fractional quantum numbers of space group symmetry. In particular, spinons can
carry fractional crystal momentum. We show that such quantum number
fractionalization has dramatic, spectroscopically accessible consequences,
namely enhanced periodicity of the two-spinon density of states in the
Brillouin zone, which can be detected via inelastic neutron scattering. This
effect is a sharp signature of certain topologically ordered spin liquids and
other symmetry enriched topological phases. Considering square lattice space
group and time reversal symmetry, we show that exactly four distinct types of
spectral periodicity are possible.Comment: 6 pages; v2: added reference; v3: improved introduction, typos
corrected; v4: added referenc
Antiferromagnetic topological insulators in cold atomic gases
We propose a spin-dependent optical lattice potential that realizes a
three-dimensional antiferromagnetic topological insulator in a gas of cold,
two-state fermions such as alkaline earths, as well as a model that describes
the tight-binding limit of this potential. We discuss the physically observable
responses of the gas that can verify the presence of this phase. We also point
out how this model can be used to obtain two-dimensional flat bands with
nonzero Chern number.Comment: 5 page
Magnetoelectric polarizability and axion electrodynamics in crystalline insulators
The orbital motion of electrons in a three-dimensional solid can generate a
pseudoscalar magnetoelectric coupling , a fact we derive for the
single-particle case using a recent theory of polarization in weakly
inhomogeneous materials. This polarizability is the same parameter
that appears in the "axion electrodynamics" Lagrangian , which is known to describe the
unusual magnetoelectric properties of the three-dimensional topological
insulator (). We compute for a simple model that accesses
the topological insulator and discuss its connection to the surface Hall
conductivity. The orbital magnetoelectric polarizability can be generalized to
the many-particle wavefunction and defines the 3D topological insulator, like
the IQHE, in terms of a topological ground-state response function.Comment: 4 pages; minor changes resulting from a change in one referenc
Magnetic phase diagram of a spin-1 condensate in two dimensions with dipole interaction
Several new features arise in the ground-state phase diagram of a spin-1
condensate trapped in an optical trap when the magnetic dipole interaction
between the atoms is taken into account along with confinement and spin
precession. The boundaries between the regions of ferromagnetic and polar
phases move as the dipole strength is varied and the ferromagnetic phases can
be modulated. The magnetization of the ferromagnetic phase perpendicular to the
field becomes modulated as a helix winding around the magnetic field direction,
with a wavelength inversely proportional to the dipole strength. This
modulation should be observable for current experimental parameters in
Rb. Hence the much-sought supersolid state, with broken continuous
translation invariance in one direction and broken global U(1) invariance,
occurs generically as a metastable state in this system as a result of dipole
interaction. The ferromagnetic state parallel to the applied magnetic field
becomes striped in a finite system at strong dipolar coupling.Comment: 11 pages, 7 figures;published versio
Delocalization of boundary states in disordered topological insulators
We use the method of bulk-boundary correspondence of topological invariants to show that disordered topological insulators have at least one delocalized state at their boundary at zero energy. Those insulators which do not have chiral (sublattice) symmetry have in addition the whole band of delocalized states at their boundary, with the zero energy state lying in the middle of the band. This result was previously conjectured based on the anticipated properties of the supersymmetric (or replicated) sigma models with WZW-type terms, as well as verified in some cases using numerical simulations and a variety of other arguments. Here we derive this result generally, in arbitrary number of dimensions, and without relying on the description in the language of sigma models
Z2 topological invariants in two dimensions from quantum Monte Carlo
We employ quantum Monte Carlo techniques to calculate the topological
invariant in a two-dimensional model of interacting electrons that exhibits a
quantum spin Hall topological insulator phase. In particular, we consider the
parity invariant for inversion-symmetric systems, which can be obtained from
the bulk's imaginary-time Green's function after an appropriate continuation to
zero frequency. This topological invariant is used here in order to study the
trivial-band to topological-insulator transitions in an interacting system with
spin-orbit coupling and an explicit bond dimerization. We discuss the
accessibility and behavior of this topological invariant within quantum Monte
Carlo simulations.Comment: 7 pages, 6 figure
Orbital magnetoelectric coupling in band insulators
Magnetoelectric responses are a fundamental characteristic of materials that
break time-reversal and inversion symmetries (notably multiferroics) and,
remarkably, of "topological insulators" in which those symmetries are unbroken.
Previous work has shown how to compute spin and lattice contributions to the
magnetoelectric tensor. Here we solve the problem of orbital contributions by
computing the frozen-lattice electronic polarization induced by a magnetic
field. One part of this response (the "Chern-Simons term") can appear even in
time-reversal-symmetric materials and has been previously shown to be quantized
in topological insulators. In general materials there are additional orbital
contributions to all parts of the magnetoelectric tensor; these vanish in
topological insulators by symmetry and also vanish in several simplified models
without time-reversal and inversion those magnetoelectric couplings were
studied before. We give two derivations of the response formula, one based on a
uniform magnetic field and one based on extrapolation of a long-wavelength
magnetic field, and discuss some of the consequences of this formula.Comment: 13 page
Topological invariants and interacting one-dimensional fermionic systems
We study one-dimensional, interacting, gapped fermionic systems described by
variants of the Peierls-Hubbard model and characterize their phases via a
topological invariant constructed out of their Green's functions. We
demonstrate that the existence of topologically protected, zero-energy states
at the boundaries of these systems can be tied to the values of their
topological invariant, just like when working with the conventional,
noninteracting topological insulators. We use a combination of analytical
methods and the numerical density matrix renormalization group method to
calculate the values of the topological invariant throughout the phase diagrams
of these systems, thus deducing when topologically protected boundary states
are present. We are also able to study topological states in spin systems
because, deep in the Mott insulating regime, these fermionic systems reduce to
spin chains. In this way, we associate the zero-energy states at the end of an
antiferromagnetic spin-one Heisenberg chain with the topological invariant 2.Comment: 15 pages, 11 figures, Final Version as published in PR