42 research outputs found
The TQ equation of the 8 vertex model for complex elliptic roots of unity
We extend our studies of the TQ equation introduced by Baxter in his 1972
solution of the 8 vertex model with parameter given by
from to the more general case of complex
We find that there are several different cases depending on the parity of
and .Comment: 30 pages, LATE
General scalar products in the arbitrary six-vertex model
In this work we use the algebraic Bethe ansatz to derive the general scalar
product in the six-vertex model for generic Boltzmann weights. We performed
this calculation using only the unitarity property, the Yang-Baxter algebra and
the Yang-Baxter equation. We have derived a recurrence relation for the scalar
product. The solution of this relation was written in terms of the domain wall
partition functions. By its turn, these partition functions were also obtained
for generic Boltzmann weights, which provided us with an explicit expression
for the general scalar product.Comment: 24 page
Extended two-level quantum dissipative system from bosonization of the elliptic spin-1/2 Kondo model
We study the elliptic spin-1/2 Kondo model (spin-1/2 fermions in one
dimension with fully anisotropic contact interactions with a magnetic impurity)
in the light of mappings to bosonic systems using the fermion-boson
correspondence and associated unitary transformations. We show that for fixed
fermion number, the bosonic system describes a two-level quantum dissipative
system with two noninteracting copies of infinitely-degenerate upper and lower
levels. In addition to the standard tunnelling transitions, and the transitions
driven by the dissipative coupling, there are also bath-mediated transitions
between the upper and lower states which simultaneously effect shifts in the
horizontal degeneracy label. We speculate that these systems could provide new
examples of continuous time quantum random walks, which are exactly solvable.Comment: 7 pages, 1 figur
Difference Equations and Highest Weight Modules of U_q[sl(n)]
The quantized version of a discrete Knizhnik-Zamolodchikov system is solved
by an extension of the generalized Bethe Ansatz. The solutions are constructed
to be of highest weight which means they fully reflect the internal quantum
group symmetry.Comment: 9 pages, LaTeX, no figure
Deconfined quantum criticality and generalised exclusion statistics in a non-hermitian BCS model
We present a pairing Hamiltonian of the Bardeen-Cooper-Schrieffer form which
exhibits two quantum critical lines of deconfined excitations. This conclusion
is drawn using the exact Bethe ansatz equations of the model which admit a
class of simple, analytic solutions. The deconfined excitations obey
generalised exclusion statistics. A notable property of the Hamiltonian is that
it is non-hermitian. Although it does not have a real spectrum for all choices
of coupling parameters, we provide a rigorous argument to establish that real
spectra occur on the critical lines. The critical lines are found to be
invariant under a renormalisation group map.Comment: 7 pages, 1 figure. Stylistic changes, results unchange
An elliptic current operator for the 8 vertex model
We compute the operator which creates the missing degenerate states in the
algebraic Bethe ansatz of the 8 vertex model at roots of unity and relate it to
the concept of an elliptic current operator. We find that in sharp contrast
with the corresponding formalism in the six-vertex model at roots of unity the
current operator is not nilpotent with the consequence that in the construction
of degenerate eigenstates of the transfer matrix an arbitrary number of exact
strings can be added to the set of regular Bethe roots. Thus the original set
of free parameters {s,t} of an eigenvector of T is enlarged to become
{s,t,\lambda_{c,1}, ..., \lambda_{c,n}\} with arbitrary string centers
\lambda_{c,j} and arbitrary n.Comment: 16 pages, Latex typographic errors corrected, text added, reference
added, accepted by Journal of Physics A,Mathematical and Genera
Functional relations for the six vertex model with domain wall boundary conditions
In this work we demonstrate that the Yang-Baxter algebra can also be employed
in order to derive a functional relation for the partition function of the six
vertex model with domain wall boundary conditions. The homogeneous limit is
studied for small lattices and the properties determining the partition
function are also discussed.Comment: 19 pages, v2: typos corrected, new section and appendix added. v3:
minor corrections, to appear in J. Stat. Mech
Backlund transformations for difference Hirota equation and supersymmetric Bethe ansatz
We consider GL(K|M)-invariant integrable supersymmetric spin chains with
twisted boundary conditions and elucidate the role of Backlund transformations
in solving the difference Hirota equation for eigenvalues of their transfer
matrices. The nested Bethe ansatz technique is shown to be equivalent to a
chain of successive Backlund transformations "undressing" the original problem
to a trivial one.Comment: 22 pages, 2 figures, based on the talk given at the Workshop
"Classical and Quantum Integrable Systems", Dubna, January 200
A variational approach for the Quantum Inverse Scattering Method
We introduce a variational approach for the Quantum Inverse Scattering Method
to exactly solve a class of Hamiltonians via Bethe ansatz methods. We undertake
this in a manner which does not rely on any prior knowledge of integrability
through the existence of a set of conserved operators. The procedure is
conducted in the framework of Hamiltonians describing the crossover between the
low-temperature phenomena of superconductivity, in the
Bardeen-Cooper-Schrieffer (BCS) theory, and Bose-Einstein condensation (BEC).
The Hamiltonians considered describe systems with interacting Cooper pairs and
a bosonic degree of freedom. We obtain general exact solvability requirements
which include seven subcases which have previously appeared in the literature.Comment: 18 pages, no eps figure
Further solutions of critical ABF RSOS models
The restricted SOS model of Andrews, Baxter and Forrester has been studied.
The finite size corrections to the eigenvalue spectra of the transfer matrix of
the model with a more general crossing parameter have been calculated.
Therefore the conformal weights and the central charges of the non-unitary or
unitary minimal conformal field have been extracted from the finite size
corrections.Comment: Pages 11; revised versio