102 research outputs found

### Analytical results for the Coqblin-Schrieffer model with generalized magnetic fields

Using the approach alternative to the traditional Thermodynamic Bethe Ansatz,
we derive analytical expressions for the free energy of Coqblin-Schrieffer
model with arbitrary magnetic and crystal fields. In Appendix we discuss two
concrete examples including the field generated crossover from the SU(4) to the
SU(2) symmetry in the SU(4)-symmetric model.Comment: 5 page

### Particles and strings in a (2+1)-D integrable quantum model

We give a review of some recent work on generalization of the Bethe ansatz in
the case of $2+1$-dimensional models of quantum field theory. As such a model,
we consider one associated with the tetrahedron equation, i.e. the
$2+1$-dimensional generalization of the famous Yang--Baxter equation. We
construct some eigenstates of the transfer matrix of that model. There arise,
together with states composed of point-like particles analogous to those in the
usual $1+1$-dimensional Bethe ansatz, new string-like states and
string-particle hybrids

### Excited State TBA for the $\phi_{2,1}$ perturbed $M_{3,5}$ model

We examine some excited state energies in the non-unitary integrable quantum
field theory obtained from the perturbation of the minimal conformal field
theory model $M_{3,5}$ by its operator $\phi_{2,1}$. Using the correspondence
of this IQFT to the scaling limit of the dilute $A_2$ lattice model (in a
particular regime) we derive the functional equations for the QFT commuting
transfer matrices. These functional equations can be transformed to a closed
set of TBA-like integral equations which determine the excited state energies
in the finite-size system. In particular, we explicitly construct these
equations for the ground state and two lowest excited states. Numerical results
for the associated energy gaps are compared with those obtained by the
truncated conformal space approach (TCSA).Comment: LaTeX, 32 pages, 6 figure

### Roots of Unity: Representations of Quantum Groups

Representations of Quantum Groups U_q (g_n), g_n any semi simple Lie algebra
of rank n, are constructed from arbitrary representations of rank n-1 quantum
groups for q a root of unity. Representations which have the maximal dimension
and number of free parameters for irreducible representations arise as special
cases.Comment: 23 page

### Some exact results for the three-layer Zamolodchikov model

In this paper we continue the study of the three-layer Zamolodchikov model
started in our previous works. We analyse numerically the solutions to the
Bethe ansatz equations. We consider two regimes I and II which differ by the
signs of the spherical sides (a1,a2,a3)->(-a1,-a2,-a3). We accept the two-line
hypothesis for the regime I and the one-line hypothesis for the regime II. In
the thermodynamic limit we derive integral equations for distribution densities
and solve them exactly. We calculate the partition function for the three-layer
Zamolodchikov model and check a compatibility of this result with the
functional relations. We also do some numerical checkings of our results.Comment: LaTeX, 27 pages, 9 figure

### On discrete integrable equations with convex variational principles

We investigate the variational structure of discrete Laplace-type equations
that are motivated by discrete integrable quad-equations. In particular, we
explain why the reality conditions we consider should be all that are
reasonable, and we derive sufficient conditions (that are often necessary) on
the labeling of the edges under which the corresponding generalized discrete
action functional is convex. Convexity is an essential tool to discuss
existence and uniqueness of solutions to Dirichlet boundary value problems.
Furthermore, we study which combinatorial data allow convex action functionals
of discrete Laplace-type equations that are actually induced by discrete
integrable quad-equations, and we present how the equations and functionals
corresponding to (Q3) are related to circle patterns.Comment: 39 pages, 8 figures. Revision of the whole manuscript, reorder of
sections. Major changes due to additional reality conditions for (Q3) and
(Q4): new Section 2.3; Theorem 1 and Sections 3.5, 3.6, 3.7 update

### Thermodynamic Bethe Ansatz for the subleading magnetic perturbation of the tricritical Ising model

We give further support to Smirnov's conjecture on the exact kink S-matrix
for the massive Quantum Field Theory describing the integrable perturbation of
the c=0.7 minimal Conformal Field theory (known to describe the tri-critical
Ising model) by the operator $\phi_{2,1}$. This operator has conformal
dimensions $(7/16,7/16)$ and is identified with the subleading magnetic
operator of the tri-critical Ising model. In this paper we apply the
Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by
explicitly utilising its relationship with the solvable lattice hard hexagon
model. Analytically examining the ultraviolet scaling limit we recover the
expected central charge c=0.7 of the tri-critical Ising model. We also compare
numerical values for the ground state energy of the finite size system obtained
from the TBA equations with the results obtained by the Truncated Conformal
Space Approach and Conformal Perturbation Theory.Comment: 22 pages, minor changes, references added. LaTeX file and postscript
figur

### Exact conserved quantities on the cylinder I: conformal case

The nonlinear integral equations describing the spectra of the left and right
(continuous) quantum KdV equations on the cylinder are derived from integrable
lattice field theories, which turn out to allow the Bethe Ansatz equations of a
twisted ``spin -1/2'' chain. A very useful mapping to the more common nonlinear
integral equation of the twisted continuous spin $+1/2$ chain is found. The
diagonalization of the transfer matrix is performed. The vacua sector is
analysed in detail detecting the primary states of the minimal conformal models
and giving integral expressions for the eigenvalues of the transfer matrix.
Contact with the seminal papers \cite{BLZ, BLZ2} by Bazhanov, Lukyanov and
Zamolodchikov is realised. General expressions for the eigenvalues of the
infinite-dimensional abelian algebra of local integrals of motion are given and
explicitly calculated at the free fermion point.Comment: Journal version: references added and minor corrections performe

### Bethe Ansatz and boundary energy of the open spin-1/2 XXZ chain

We review recent results on the Bethe Ansatz solutions for the eigenvalues of
the transfer matrix of an integrable open XXZ quantum spin chain using
functional relations which the transfer matrix obeys at roots of unity. First,
we consider a case where at most two of the boundary parameters
{{$\alpha_-$,$\alpha_+$,$\beta_-$,$\beta_+$}} are nonzero. A generalization of
the Baxter $T-Q$ equation that involves more than one independent $Q$ is
described. We use this solution to compute the boundary energy of the chain in
the thermodynamic limit. We conclude the paper with a review of some results
for the general integrable boundary terms, where all six boundary parameters
are arbitrary.Comment: 6 pages, Latex; contribution to the XVth International Colloquium on
Integrable Systems and Quantum Symmetries, Prague, June 2006. To appear in
Czechoslovak Journal of Physics (2006); (v2) Typos corrected and a new line
added in the Acknowledgments sectio

### Exact conserved quantities on the cylinder II: off-critical case

With the aim of exploring a massive model corresponding to the perturbation
of the conformal model [hep-th/0211094] the nonlinear integral equation for a
quantum system consisting of left and right KdV equations coupled on the
cylinder is derived from an integrable lattice field theory. The eigenvalues of
the energy and of the transfer matrix (and of all the other local integrals of
motion) are expressed in terms of the corresponding solutions of the nonlinear
integral equation. The analytic and asymptotic behaviours of the transfer
matrix are studied and given.Comment: enlarged version before sending to jurnal, second part of
hep-th/021109

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