arXiv subjects

G. Sierra

Publications and source records attributed to G. Sierra.

58 records · Page 4Linked to original sources

arXiv1992

q--Magnetism at roots of unity

We study the thermodynamic properties of a family of integrable 1D spin chain hamiltonians associated with quantum groups at roots of unity. These hamiltonians depend for each primitive root of unit on a parameter $s$ which plays the role of a continuous spin. The model exhibits ferrimagnetism even though the interaction involved is between nearest neighbors. The latter phenomenon is interpreted as a genuine quantum group effect with no ``classical" analog. The discussion of conformal properties is given.

hep-th↗

arXiv1992

On Integrable Quantum Group Invariant Antiferromagnets

A new open spin chain hamiltonian is introduced. It is both integrable (Sklyanin`s type $K$ matrices are used to achieve this) and invariant under ${\cal U}_ε(sl(2))$ transformations in nilpotent irreps for $ε^3=1$. Some considerations on the centralizer of nilpotent representations and its representation theory are also presented.

hep-th↗

arXiv1992

New Integrable Deformations of Higher Spin Heisenberg-Ising Chains

We show that the anisotropic Heisenberg-Ising chains with higher spin allow, for special values of the anisotropy, integrable deformations intimately related to the theory of quantum groups at roots of unity. For the spin one case we construct and study the symmetries of the hamiltonian which depends on a spectral variable belonging to an elliptic curve. One of the points of this curve yields the Fateev-Zamolodchikov hamiltonian of spin one and anisotropy $Δ= \frac{ q^2 + q^{-2}}{2} $ with $q$ a cubic root of unity. In some other special points the spin degrees of freedom as well as the hamiltonian splits into pieces governed by a larger symmetry.

hep-th↗

arXiv1991

Quantum Harmonic Oscillator Algebra and Link Invariants

The $q$--deformation $U_q (h_4)$ of the harmonic oscillator algebra is defined and proved to be a Ribbon Hopf algebra.Associated with this Hopf algebra we define an infinite dimensional braid group representation on the Hilbert space of the harmonic oscillator, and an extended Yang--Baxter system in the sense of Turaev. The corresponding link invariant is computed in some particular cases and coincides with the inverse of the Alexander--Conway polynomial. The $R$ matrix of $U_q (h_4)$ can be interpreted as defining a baxterization of the intertwiners for semicyclic representations of $SU(2)_q$ at $q=e^{2 πi/N}$ in the $N \rightarrow \infty$ limit.Finally we define new multicolored braid group representations and study their relation to the multivariable Alexander--Conway polynomial.

hep-th↗