Bloch Hamiltonians and topologically ordered states

We consider a universal representation for the Hamiltonian of systems in topologically ordered phase states. We show that for strongly correlated electronic systems, the Hamiltonian expressed in terms of projectors of the Temperley-Lieb algebra on the spin singlet state has the form of a two-dimensional Bloch matrix in the case of doubly linked excitation world lines; in this case, different topological orderings are separated by a quantum critical point where the matrix elements of the Hamiltonian vanish. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 160, No. 1, pp. 220–228, July, 2009.