379 research outputs found
The -anyon chain: integrable boundary conditions and excitation spectra
Chains of interacting non-Abelian anyons with local interactions invariant
under the action of the Drinfeld double of the dihedral group are
constructed. Formulated as a spin chain the Hamiltonians are generated from
commuting transfer matrices of an integrable vertex model for periodic and
braided as well as open boundaries. A different anyonic model with the same
local Hamiltonian is obtained within the fusion path formulation. This model is
shown to be related to an integrable fusion interaction round the face model.
Bulk and surface properties of the anyon chain are computed from the Bethe
equations for the spin chain. The low energy effective theories and operator
content of the models (in both the spin chain and fusion path formulation) are
identified from analytical and numerical studies of the finite size spectra.
For all boundary conditions considered the continuum theory is found to be a
product of two conformal field theories. Depending on the coupling constants
the factors can be a parafermion or a minimal
model.Comment: Major revisions have been mad
Integrable anyon chains: from fusion rules to face models to effective field theories
Starting from the fusion rules for the algebra we construct
one-dimensional lattice models of interacting anyons with commuting transfer
matrices of `interactions round the face' (IRF) type. The conserved topological
charges of the anyon chain are recovered from the transfer matrices in the
limit of large spectral parameter. The properties of the models in the
thermodynamic limit and the low energy excitations are studied using Bethe
ansatz methods. Two of the anyon models are critical at zero temperature. From
the analysis of the finite size spectrum we find that they are effectively
described by rational conformal field theories invariant under extensions of
the Virasoro algebra, namely and ,
respectively. The latter contains primaries with half and quarter spin. The
modular partition function and fusion rules are derived and found to be
consistent with the results for the lattice model.Comment: 43 pages, published versio
Quantum phases of a chain of strongly interacting anyons
We study a strongly interacting chain of anyons with fusion rules determined
by SO(5)2. The phase portrait is identified with a combination of numerical and
analytical techniques. Several critical phases with different central charges
and their corresponding transitions identified.Comment: 5 pages, 4 figure
Collective states of interacting non-Abelian anyons
We study the finite size spectrum of integrable quantum chains of interacting
non-Abelian anyons constructed using the Drinfeld double of the dihedral group
. The gapless low energy modes are identified as the direct product of two
conformal field theories which can be decomposed according to the residual
symmetries of the chains subject to periodic boundary conditions.Comment: 11 page
Exact solution of the D3 non-Abelian anyon chain
Commuting transfer matrices for linear chains of interacting non-Abelian anyons from the two-dimensional irreducible representation of the dihedral group D3 [or, equivalently, the integer sector of the su(2)4 spin-1 chain] are constructed using the spin-anyon correspondence to a D3-symmetric formulation of the XXZ Heisenberg spin chain. The spectral problem is solved using discrete inversion identities satisfied by these transfer matrices and functional Bethe ansatz methods. The resulting spectrum can be related to that of the XXZ spin-1/2 Heisenberg chain with boundary conditions depending on the topological sector of the anyon chain. The properties of this model in the critical regime are studied by finite size analysis of the spectrum. In particular, points in the phase diagram where the anyon chain realizes some of the rational Z2 orbifold theories are identified
From spin to anyon notation: The XXZ Heisenberg model as a (or ) anyon chain
We discuss a relationship between certain one-dimensional quantum spin chains
and anyon chains. In particular we show how the XXZ Heisenberg chain is
realised as a (alternately ) anyon model. We find the
difference between the models lie primarily in choice of boundary condition.Comment: 13 page
2D and 3D reconstructions in acousto-electric tomography
We propose and test stable algorithms for the reconstruction of the internal
conductivity of a biological object using acousto-electric measurements.
Namely, the conventional impedance tomography scheme is supplemented by
scanning the object with acoustic waves that slightly perturb the conductivity
and cause the change in the electric potential measured on the boundary of the
object. These perturbations of the potential are then used as the data for the
reconstruction of the conductivity. The present method does not rely on
"perfectly focused" acoustic beams. Instead, more realistic propagating
spherical fronts are utilized, and then the measurements that would correspond
to perfect focusing are synthesized. In other words, we use \emph{synthetic
focusing}. Numerical experiments with simulated data show that our techniques
produce high quality images, both in 2D and 3D, and that they remain accurate
in the presence of high-level noise in the data. Local uniqueness and stability
for the problem also hold
Induced Topological Phases at the Boundary of 3D Topological Superconductors
We present tight-binding models of 3D topological superconductors in class DIII that support a variety of winding numbers. We show that gapless Majorana surface states emerge at their boundary in agreement with the bulk-boundary correspondence. At the presence of a Zeeman field, the surface states become gapped and the boundary behaves as a 2D superconductor in class D. Importantly, the 2D and 3D winding numbers are in agreement, signifying that the topological phase of the boundary is induced by the phase of the 3D bulk. Hence, the boundary of a 3D topological superconductor in class DIII can be used for the robust realization of localized Majorana zero modes
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