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We conjecture exact and simple formulas for physical quantities in twoquantum chains. A classic result of this type is Onsager, Kaufman and Yang'sformula for the spontaneous magnetization in the Ising model, subsequentlygeneralized to the chiral Potts models. We conjecture that analogous resultsoccur in the XYZ chain when the couplings obey J_xJ_y + J_yJ_z + J_x J_z=0, andin a related fermion chain with strong interactions and supersymmetry. We findexact formulas for the magnetization and gap in the former, and the staggereddensity in the latter, by exploiting the fact that certain quantities areindependent of finite-size effects.

Exact and simple results for the XYZ and strongly interacting fermion chains