1,001 research outputs found
Exact results for spin dynamics and fractionization in the Kitaev Model
We present certain exact analytical results for dynamical spin correlation
functions in the Kitaev Model. It is the first result of its kind in
non-trivial quantum spin models. The result is also novel: in spite of presence
of gapless propagating Majorana fermion excitations, dynamical two spin
correlation functions are identically zero beyond nearest neighbor separation,
showing existence of a gapless but short range spin liquid. An unusual,
\emph{all energy scale fractionization}of a spin -flip quanta, into two
infinitely massive -fluxes and a dynamical Majorana fermion, is shown to
occur. As the Kitaev Model exemplifies topological quantum computation, our
result presents new insights into qubit dynamics and generation of topological
excitations.Comment: 4 pages, 2 figures. Typose corrected, figure made better, clarifying
statements and references adde
Friedel oscillations due to Fermi arcs in Weyl semimetals
Weyl semimetals harbor unusual surface states known as Fermi arcs, which are
essentially disjoint segments of a two dimensional Fermi surface. We describe a
prescription for obtaining Fermi arcs of arbitrary shape and connectivity by
stacking alternate two dimensional electron and hole Fermi surfaces and adding
suitable interlayer coupling. Using this prescription, we compute the local
density of states -- a quantity directly relevant to scanning tunneling
microscopy -- on a Weyl semimetal surface in the presence of a point scatterer
and present results for a particular model that is expected to apply to
pyrochlore iridate Weyl semimetals. For thin samples, Fermi arcs on opposite
surfaces conspire to allow nested backscattering, resulting in strong Friedel
oscillations on the surface. These oscillations die out as the sample thickness
is increased and Fermi arcs from the bottom surface retreat and weak
oscillations, due to scattering between the top surface Fermi arcs alone,
survive. The surface spectral function -- accessible to photoemission
experiments -- is also computed. In the thermodynamic limit, this calculation
can be done analytically and separate contributions from the Fermi arcs and the
bulk states can be seen.Comment: 5 pages, 2 figures; minor changes in figures and text, typos
correcte
Symmetry and Topological Order
We prove sufficient conditions for Topological Quantum Order at both zero and
finite temperatures. The crux of the proof hinges on the existence of
low-dimensional Gauge-Like Symmetries (that notably extend and differ from
standard local gauge symmetries) and their associated defects, thus providing a
unifying framework based on a symmetry principle. These symmetries may be
actual invariances of the system, or may emerge in the low-energy sector.
Prominent examples of Topological Quantum Order display Gauge-Like Symmetries.
New systems exhibiting such symmetries include Hamiltonians depicting
orbital-dependent spin exchange and Jahn-Teller effects in transition metal
orbital compounds, short-range frustrated Klein spin models, and p+ip
superconducting arrays. We analyze the physical consequences of Gauge-Like
Symmetries (including topological terms and charges), discuss associated
braiding, and show the insufficiency of the energy spectrum, topological
entanglement entropy, maximal string correlators, and fractionalization in
establishing Topological Quantum Order. General symmetry considerations
illustrate that not withstanding spectral gaps, thermal fluctuations may impose
restrictions on certain suggested quantum computing schemes and lead to
"thermal fragility". Our results allow us to go beyond standard topological
field theories and engineer systems with Topological Quantum Order.Comment: 10 pages, 2 figures. Minimal changes relative to published version-
most notably the above shortened title (which was too late to change upon
request in the galley proofs). An elaborate description of all of the results
in this article appeared in subsequent works, principally in
arXiv:cond-mat/0702377 which was published in the Annals of Physics 324, 977-
1057 (2009
Detecting non-Abelian Statistics with Electronic Mach-Zehnder Interferometer
Fractionally charged quasiparticles in the quantum Hall state with filling
factor are expected to obey non-Abelian statistics. We demonstrate
that their statistics can be probed by transport measurements in an electronic
Mach-Zehnder interferometer. The tunneling current through the interferometer
exhibits a characteristic dependence on the magnetic flux and a non-analytic
dependence on the tunneling amplitudes which can be controlled by gate
voltages.Comment: 4 pages, 2 figures; Revtex; a discussion of the asymmetry of the I-V
curve adde
Quantum simulators, continuous-time automata, and translationally invariant systems
The general problem of finding the ground state energy of lattice
Hamiltonians is known to be very hard, even for a quantum computer. We show
here that this is the case even for translationally invariant systems. We also
show that a quantum computer can be built in a 1D chain with a fixed,
translationally invariant Hamitonian consisting of nearest--neighbor
interactions only. The result of the computation is obtained after a prescribed
time with high probability.Comment: partily rewritten and important references include
Connection Formulae for Asymptotics of Solutions of the Degenerate Third Painlev\'{e} Equation. I
The degenerate third Painlev\'{e} equation, , where ,
and , and the associated tau-function are studied via the
Isomonodromy Deformation Method. Connection formulae for asymptotics of the
general as and solution and general regular as and solution are obtained.Comment: 40 pages, LaTeX2
Ettingshausen effect due to Majorana modes
The presence of Majorana zero-energy modes at vortex cores in a topological
superconductor implies that each vortex carries an extra entropy , given
by , that is independent of temperature. By utilizing this
special property of Majorana modes, the edges of a topological superconductor
can be cooled (or heated) by the motion of the vortices across the edges. As
vortices flow in the transverse direction with respect to an external imposed
supercurrent, due to the Lorentz force, a thermoelectric effect analogous to
the Ettingshausen effect is expected to occur between opposing edges. We
propose an experiment to observe this thermoelectric effect, which could
directly probe the intrinsic entropy of Majorana zero-energy modes.Comment: 16 pages, 3 figure
Spin Berry phase in the Fermi arc states
Unusual electronic property of a Weyl semi-metallic nanowire is revealed. Its
band dispersion exhibits multiple subbands of partially flat dispersion,
originating from the Fermi arc states. Remarkably, the lowest energy flat
subbands bear a finite size energy gap, implying that electrons in the Fermi
arc surface states are susceptible of the spin Berry phase. This is shown to be
a consequence of spin-to-surface locking in the surface electronic states. We
verify this behavior and the existence of spin Berry phase in the low-energy
effective theory of Fermi arc surface states on a cylindrical nanowire by
deriving the latter from a bulk Weyl Hamiltonian. We point out that in any
surface state exhibiting a spin Berry phase pi, a zero-energy bound state is
formed along a magnetic flux tube of strength, hc/(2e). This effect is
highlighted in a surfaceless bulk system pierced by a dislocation line, which
shows a 1D chiral mode along the dislocation line.Comment: 9 pages, 9 figure
Topological entropy of realistic quantum Hall wave functions
The entanglement entropy of the incompressible states of a realistic quantum
Hall system are studied by direct diagonalization. The subdominant term to the
area law, the topological entanglement entropy, which is believed to carry
information about topologic order in the ground state, was extracted for
filling factors 1/3, 1/5 and 5/2. The results for 1/3 and 1/5 are consistent
with the topological entanglement entropy for the Laughlin wave function. The
5/2 state exhibits a topological entanglement entropy consistent with the
Moore-Read wave function.Comment: 6 pages, 6 figures; improved computations and graphics; added
reference
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