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Abstract

Several generalizations of one-dimensional and two-dimensional exactly solvable low-dimensional quantum spin-1/2 models, some of which contain off-diagonal terms of the exchange tensor, are proposed. It is shown that off-diagonal terms of the exchange (symmetric or nonsymmetric with respect to the exchange of spins) yield renormalization of the diagonal ones and phase shifts. The latter can be moved to eigenfunctions of the models and do not affect eigenvalues for open geometries of the lattices. For closed geometries of the lattices the phase shifts manifest themselves in the finite size corrections. The advantage of the proposed models is in their simplicity and in possible realizations of the models in a number of applications, e.g., for the description of the wide variety of correlated electron systems, ultracold atoms, and in the theory of topological quantum computation.