A family of subfactors arising from a pair of complex Hadamard matrices

In this paper, we define a new equivalence relation ‘[Formula: see text]’ on the set of all Hadamard inequivalent complex Hadamard matrices of order [Formula: see text] and show that pairs [Formula: see text] of equivalent matrices [Formula: see text] produce an infinite family of potentially new subfactors of the hyperfinite type [Formula: see text] factor [Formula: see text]. All these subfactors are irreducible with the Jones index [Formula: see text], including all possibilities. We also show that this family contains infinitely many infinite-depth subfactors. As an application, we compute the Connes–Størmer relative entropy and the angle between the pair [Formula: see text] of spin model subfactors arising from the pair [Formula: see text] of equivalent matrices. On the other hand, pairs [Formula: see text] of inequivalent matrices [Formula: see text] lead to subalgebras of [Formula: see text] with infinite Pimsner–Popa index.