Luca Mezincescu

Fusion procedure for open chains

The authors have generalized Sklyanins approach of constructing open integrable quantum spin chains to the case of PT-invariant R matrices. They formulate a fusion procedure for such chains. In particular, they show that the fused transfer matrix can be expressed in terms of products of the original transfer matrix and products of certain quantum determinants which can be explicitly evaluated. Applications of these results include constructing open integrable higher-spin chains, as well as obtaining functional equations for transfer-matrix eigenvalues, which may be solved by an analytical Bethe ansatz.

Bethe Ansatz Solution of the Fateev-zamolodchikov Quantum Spin Chain With Boundary Terms

Abstract We solve the Fateev-Zamolodchikov quantum spin chain (i.e., the spin-1 XXZ quantum Heisenberg chain) with a class of boundary terms by the quantum inverse scattering method. For a particular choice of boundary terms, the model has the quantum symmetry U q [SU (2)].

Analytical Bethe Ansatz for quantum-algebra-invariant spin chains

Abstract We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz (BA) method. In particular, we determine in this way the spectrum of the transfer matrices of the U q [su(2)]-invariant spin chains associated with A 1 (1) and A 2 (2) in the fundamental representation. The quantum-algebra invariance of these models plays an essential role in obtaining these results. The BA equations for these open chains are “doubled” with respect to the BA equations for the corresponding closed chains.

Integrability of open spin chains with quantum algebra symmetry

In this paper, the authors prove that certain quantum spin chains with quantum-algebra symmetry are integrable. Specifically these are the quantum-algebra-invariant open chains associated with the affine Lie algebras A[sub 1][sup (1)], A[sub 2n][sup (2)], A[sub 2n [minus] 1][sup (2)], B[sub n][sup (1)], C[sub n][sup (1)], and D[sub n][sup (1)] in the fundamental representation. Conspicuously absent from this list is A[sub n][sup (1)] for n [gt] 1. This is because in order to demonstrate integrability, the authors assume that the corresponding R matrix has crossing symmetry, which is not true in the case A[sub n][sup (1)] for n [gt] 1.

Biorthogonal quantum systems

Models of PT symmetric quantum mechanics provide examples of biorthogonal quantum systems. The latter incorporate all the structure of PT symmetric models, and allow for generalizations, especially in situations where the PT construction of the dual space fails. The formalism is illustrated by a few exact results for models of the form H=(p+ν)2+∑k>0μkexp(ikx). In some nontrivial cases, equivalent Hermitian theories are obtained and shown to be very simple: They are just free (chiral) particles. Field theory extensions are briefly considered.

Non-relativistic strings and branes as non-linear realizations of Galilei groups

Abstract We construct actions for non-relativistic strings and membranes purely as Wess–Zumino terms of the underlying Galilei groups.

THERMODYNAMICS OF INTEGRABLE CHAINS WITH ALTERNATING SPINS

We consider a two-parameter

Anyons from Strings

(\bar c, \tilde c)

Classical and quantal ternary algebras

family of quantum integrable Hamiltonians for a chain of alternating spins of spin

QUANTUM ALGEBRA STRUCTURE OF EXACTLY SOLUBLE QUANTUM SPIN CHAINS

s=1/2