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A Temperley-Lieb algebra is extracted from the operator structure of a newclass of $N^{2}\times N^{2}$ braid matrices presented and studied in previouspapers and designated as $S\hat{O}_{(q)}(N)$, $S\hat{p}%_{(q)}(N)$ for theq-deformed orthogonal and symplectic cases respectively. Spin chainHamiltonians are derived from such braid matrices and the corresponding chainsare studied. Time evolutions of the chains and the possibility of transition ofdata encoded in the parameters of mixed states from one end to the other areanalyzed. The entanglement entropies $% S(q,N)$ of eigenstates of the crucialoperator, namely the q-dependent $% N^{2}\times N^{2}$ projector $P_{0}$appearing in the corresponding Hamiltonian are obtained. Study of entanglementsgenerated under the actions of \ $S\hat{O}(N)$, $S\hat{p}(N)$ braid operators,unitarized with imaginary rapidities is presented as a perspective.

journal of mathematical physics

New classes of spin chains from $(S\hat{O}_{(q)}(N)$,  $S\hat{p}_{(q)}(N))$ Temperley-Lieb algebras: Data transmission and (q, N)  parametrized entanglement entropies