320 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
Approximating the Sachdev-Ye-Kitaev model with Majorana wires
The Sachdev-Ye-Kitaev (SYK) model describes a collection of randomly
interacting Majorana fermions that exhibits profound connections to quantum
chaos and black holes. We propose a solid-state implementation based on a
quantum dot coupled to an array of topological superconducting wires hosting
Majorana zero modes. Interactions and disorder intrinsic to the dot mediate the
desired random Majorana couplings, while an approximate symmetry suppresses
additional unwanted terms. We use random matrix theory and numerics to show
that our setup emulates the SYK model (up to corrections that we quantify) and
discuss experimental signatures.Comment: 7 pages, 2 figure
Numerical detection of symmetry enriched topological phases with space group symmetry
Topologically ordered phases of matter, in particular so-called symmetry
enriched topological (SET) phases, can exhibit quantum number fractionalization
in the presence of global symmetry. In Z_2 topologically ordered states in two
dimensions, fundamental translations T_x and T_y acting on anyons can either
commute or anticommute. This property, crystal momentum fractionalization, can
be seen in a periodicity of the excited-state spectrum in the Brillouin zone.
We present a numerical method to detect the presence of this form of symmetry
enrichment given a projected entangled pair state (PEPS); we study the minima
of spectrum of correlation lengths of the transfer matrix for a cylinder. As a
benchmark, we demonstrate our method using a modified toric code model with
perturbation. An enhanced periodicity in momentum clearly reveals the
anticommutation relation {T_x,T_y}=0$ for the corresponding quasiparticles in
the system.Comment: 7 figs, 8 pages. Accepted by PRB rapid communicatio
Anomalous Quasiparticle Symmetries and Non-Abelian Defects on Symmetrically Gapped Surfaces of Weak Topological Insulators
We show that boundaries of 3D weak topological insulators can become gapped
by strong interactions while preserving all symmetries, leading to Abelian
surface topological order. The anomalous nature of the weak topological
insulators manifests itself in a non-trivial action of symmetries on the
quasiparticles; most strikingly, translations change the anyon types in a
manner impossible in strictly 2D systems with the same symmetry. As a further
consequence, screw dislocations form non-Abelian defects that trap
parafermion zero modes.Comment: 6 pages, 4 figure
How Do You Want That Insulator?
A normal insulator is turned into an exotic topological insulator by tuning
its elemental composition.Comment: Science Perspective article on arXiv:1104.463
Majorana spin liquids and projective realization of SU(2) spin symmetry
We revisit the fermionic parton approach to S = 1/2 quantum spin liquids with
SU(2) spin rotation symmetry, and the associated projective symmetry group
(PSG) classification. We point out that the existing PSG classification is
incomplete; upon completing it, we find spin liquid states with S=1 and S=0
Majorana fermion excitations coupled to a deconfined Z2 gauge field. The
crucial observation leading us to this result is that, like space group and
time reversal symmetries, spin rotations can act projectively on the fermionic
partons; that is, a spin rotation may be realized by simultaneous SU(2) spin
and gauge rotations. We show that there are only two realizations of spin
rotations acting on fermionic partons: the familiar naive realization where
spin rotation is not accompanied by any gauge transformation, and a single type
of projective realization. We discuss the PSG classification for states with
projective spin rotations. To illustrate these results, we show that there are
four such PSGs on the two-dimensional square lattice. We study the properties
of the corresponding states, finding that one -- with gapless Fermi points --
is a stable phase beyond mean-field theory. In this phase, depending on
parameters, a small Zeeman magnetic field can open a partial gap for the
Majorana fermion excitations. Moreover, there are nearby gapped phases
supporting Z2 vortex excitations obeying non-Abelian statistics. We conclude
with a discussion of various open issues, including the challenging question of
where such S=1 Majorana spin liquids may occur in models and in real systems.Comment: 19 pages, 8 figures. Typos corrected, references adde
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
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