Analogy Between Fractional Quantum Hall Effect and Commensurate Flux Phase States on a Lattice

Abstract

We study the analogy between fractional Quantum Hall Effect and commensurate flux phases on a lattice. We propose a variational approach for the study of these chiral flux phase states. We classify antiferromagnetic chiral flux phase states and evaluate analytically the corresponding expectation values of the t-J Hamiltonian at any value of filling. There are two types of chiral flux phase states: commensurate and fractional. We have found that state with the minimum energy is a commensurate flux phase state for which the value of the flux of the orbital magnetic field equals the filling and the total spin of this system equals zero.