R. A. Usmanov | Searcharxiv

arXiv2002

Correspondence between the XXZ model in roots of unity and the one-dimensional quantum Ising chain with different boundary conditions

We consider the integrable XXZ model with special open boundary conditions that renders its Hamiltonian ${SU(2)}_q$ symmetric, and the one-dimensional quantum Ising model with four different boundary conditions. We show that for each boundary condition the Ising quantum chain is exactly given by the Minimal Model of integrable lattice theory $LM(3, 4)$. This last theory is obtained as the result of the quantum group reduction of the XXZ model at anisotropy $Δ=(q + q^{-1})/2=\sqrt{2}/2$, with a number of sites in the latter defined by the type of boundary conditions.

hep-th↗

arXiv2001

New relations in the algebra of the Baxter Q-operators

We consider irreducible cyclic representations of the algebra of monodromy matrices corresponding to the R-matrix of the six-vertex model. In roots of unity the Baxter Q-operator can be represented as a trace of a tensor product of L-operators corresponding to one of these cyclic representations and satisfies the TQ-equation. We find a new algebraic structure generated by these L-operators and, as a consequence, by the Q-operators.

hep-th↗