34 research outputs found
Non-Hermitian spin chains with inhomogeneous coupling
An open U_q(sl_2)-invariant spin chain of spin S and length N with
inhomogeneous coupling is investigated as an example of a non-Hermitian
(quasi-Hermitian) model. For several particular cases of such a chain, the
ranges of the deformation parameter gamma are determined for which the spectrum
of the model is real. For a certain range of gamma, a universal metric operator
is constructed and thus the quasi-Hermiticity of the model is established. The
constructed metric operator is non-dynamical, its structure is determined only
by the symmetry of the model. The results apply, in particular, to all known
homogeneous U_q(sl_2)-invariant integrable spin chains with nearest-neighbour
interaction. In addition, the most general form of a metric operator for a
quasi-Hermitian operator in finite dimensional space is discussed.Comment: 19 pages, LaTeX; v.3 - a proof of eq.(52) adde
Wilson lines on noncommutative tori
We introduce the notion of a monodromy for gauge fields with vanishing
curvature on the noncommutative torus. Similar to the ordinary gauge theory,
traces of the monodromies define noncommutative Wilson lines. Our main result
is that these Wilson lines are invariant under the Seiberg-Witten map changing
the deformation parameter of the noncommutative torus.Comment: 4 pages, LaTeX (revtex), it is explained why the costruction of a
Wilson line using the path ordered exponent does not apply in the
noncommutative cas
Fermionic representations for characters of M(3,t), M(4,5), M(5,6) and M(6,7) minimal models and related Rogers-Ramanujan type and dilogarithm identities
Characters and linear combinations of characters that admit a fermionic sum
representation as well as a factorized form are considered for some minimal
Virasoro models. As a consequence, various Rogers-Ramanujan type identities are
obtained. Dilogarithm identities producing corresponding effective central
charges and secondary effective central charges are derived. Several ways of
constructing more general fermionic representations are discussed.Comment: 14 pages, LaTex; minor correction
On integrable Hamiltonians for higher spin XXZ chain
Integrable Hamiltonians for higher spin periodic XXZ chains are constructed
in terms of the spin generators; explicit examples for spins up to 3/2 are
given. Relations between Hamiltonians for some U_q(sl_2)-symmetric and
U(1)-symmetric universal r-matrices are studied; their properties are
investigated. A certain modification of the higher spin periodic chain
Hamiltonian is shown to be an integrable U_q(sl_2)-symmetric Hamiltonian for an
open chain.Comment: 20 pages, Latex; Section 8 has been modifie
Thermodynamics and conformal properties of XXZ chains with alternating spins
The quantum periodic XXZ chain with alternating spins is studied. The
properties of the related R-matrix and Hamiltonians are discussed. A compact
expression for the ground state energy is obtained. The corresponding conformal
anomaly is found via the finite-size computations and also by means of the
Bethe ansatz method. In the presence of an external magnetic field, the
magnetic susceptibility is derived. The results are also generalized to the
case of a chain containing several different spins.Comment: 28 pages, LaTeX2
Form factors of integrable Heisenberg (higher) spin chains
We present determinant formulae for the form factors of spin operators of
general integrable XXX Heisenberg spin chains for arbitrary (finite
dimensional) spin representations. The results apply to any "mixed" spin
chains, such as alternating spin chains, or to spin chains with magnetic
impurities.Comment: 24 page