arXiv subjects

S. G. Mc Ateer

Publications and source records attributed to S. G. Mc Ateer.

2 recordsLinked to original sources

arXiv2011

On factorizing $F$-matrices in $Y(sl_n)$ and $U_q(\hat{sl_n})$ spin chains

We consider quantum spin chains arising from $N$-fold tensor products of the fundamental evaluation representations of $Y(sl_n)$ and $U_q(\hat{sl_n})$. Using the partial $F$-matrix formalism from the seminal work of Maillet and Sanchez de Santos, we derive a completely factorized expression for the $F$-matrix of such models and prove its equivalence to the expression obtained by Albert, Boos, Flume and Ruhlig. A new relation between the $F$-matrices and the Bethe eigenvectors of these spin chains is given.

math-ph↗

arXiv2011

Factorizing $F$-matrices and the XXZ spin-1/2 chain: A diagrammatic perspective

Using notation inherited from the six-vertex model, we construct diagrams that represent the action of the factorizing $F$-matrices associated to the finite length XXZ spin-1/2 chain. We prove that these $F$-matrices factorize the tensor $R^σ_{1... n}$ corresponding with elements of the permutation group. We consider in particular the diagram for the tensor $R^{σ_c}_{1... n}$, which cyclically permutes the spin chain. This leads us to a diagrammatic construction of the local spin operators $S_i^{\pm}$ and $S_i^{z}$ in terms of the monodromy matrix operators.

math-ph↗