Bloch Hamiltonians and topologically ordered states

V. A. Verbus^a, L. Martina^b, A. P. Protogenov<sup>c

a</sup> Institute for Physics of Microstructures, Russian Academy of Sciences
^b Lecce University
^c Institute of Applied Physics, Russian Academy of Sciences

Abstract: 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.

Keywords: topologically ordered states, quantum phase transition, Temperley–Lieb algebra.

DOI: 10.4213/tmf6393

 English version: Theoretical and Mathematical Physics, 2009, 160:1, 1058–1065

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