BERRY PHASE IN YANG–BAXTER SYSTEMS AND BOGOLIUBOV HAMILTONIAN AS A DERIVATIVE OF DIRAC HAMILTONIAN VIA BRAID RELATION

Spin interaction Hamiltonians are obtained from the unitary Yang–Baxter Ř-matrix. Based on which, we study Berry phase and quantum criticality in the Yang–Baxter systems. We also indicate that Bogoliubov Hamiltonian is a derivative of Dirac Hamiltonian via braid relation.