1,542 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
Integro-Difference Equation for a correlation function of the spin- Heisenberg XXZ chain
We consider the Ferromagnetic-String-Formation-Probability correlation
function (FSFP) for the spin- Heisenberg XXZ chain. We construct a
completely integrable system of integro-difference equations (IDE), which has
the FSFP as a -function. We derive the associated Riemann-Hilbert problem
and obtain the large distance asymptotics of the FSFP correlator in some
limiting cases.Comment: 14 pages, latex+epsf, 1 figur
Breit-Wigner width for two interacting particles in one-dimensional random potential
For two interacting particles (TIP) in one-dimensional random potential the
dependence of the Breit-Wigner width , the local density of states and
the TIP localization length on system parameters is determined analytically.
The theoretical predictions for are confirmed by numerical
simulations.Comment: 10 pages Latex, 4 figures included. New version with extended
numerical results and discussions of earlier result
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
Determinant representation for a quantum correlation function of the lattice sine-Gordon model
We consider a completely integrable lattice regularization of the sine-Gordon
model with discrete space and continuous time. We derive a determinant
representation for a correlation function which in the continuum limit turns
into the correlation function of local fields. The determinant is then embedded
into a system of integrable integro-differential equations. The leading
asymptotic behaviour of the correlation function is described in terms of the
solution of a Riemann Hilbert Problem (RHP) related to the system of
integro-differential equations. The leading term in the asymptotical
decomposition of the solution of the RHP is obtained.Comment: 30 pages Latex2e, 2 Figures, epsf. Significantly extended and revised
versio
Spin-spin correlations between two Kondo impurities coupled to an open Hubbard chain
In order to study the interplay between Kondo and
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, we calculate the spin-spin
correlation functions between two Kondo impurities coupled to different sites
of a half-filled open Hubbard chain. Using the density-matrix renormalization
group (DMRG), we re-examine the exponents for the power-law decay of the
correlation function between the two impurity spins as a function of the
antiferromagnetic coupling J, the Hubbard interaction U, and the distance R
between the impurities. The exponents for finite systems obtained in this work
deviate from previously published DMRG calculations. We furthermore show that
the long-distance behavior of the exponents is the same for impurities coupled
to the bulk or to both ends of the chain. We note that a universal exponent for
the asymptotic behavior cannot be extracted from these finite-size systems with
open boundary conditions.Comment: 8 pages, 10 figures; v2: final version, references and Fig. 8 adde
Open t-J chain with boundary impurities
We study integrable boundary conditions for the supersymmetric t-J model of
correlated electrons which arise when combining static scattering potentials
with dynamical impurities carrying an internal degree of freedom. The latter
differ from the bulk sites by allowing for double occupation of the local
orbitals. The spectrum of the resulting Hamiltonians is obtained by means of
the algebraic Bethe Ansatz.Comment: LaTeX2e, 9p
Emergence of Quantum Ergodicity in Rough Billiards
By analytical mapping of the eigenvalue problem in rough billiards on to a
band random matrix model a new regime of Wigner ergodicity is found. There the
eigenstates are extended over the whole energy surface but have a strongly
peaked structure. The results of numerical simulations and implications for
level statistics are also discussed.Comment: revtex, 4 pages, 4 figure
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