We calculate the energy of lattice fermions with a small density moving in a weak magnetic field. It is shown that the ground state energy has a minimum at B = 2πν/ea2. Based on this fact we discuss some aspects of the modern theory of strongly correlated fermionic systems.
We calculate the ground state energies and wavefunctions for small systems of fermions on a lattice using singly and doubly periodic boundary conditions. We find minima in the ground state energy when the magnetic flux per plaquette corresponds to filling fractions with odd denominators. We interpret these minima in terms of fractional quantum Hall states. The pair correlation function at nearest and next-nearest neighbours is calculated as a function of the repulsive interaction strength between particles.
The energy of 2D Bloch electrons in a magnetic field is studied as a function of the filling fraction ν and the magnetic flux Φ. Using a new semi-classical quantization method the total energy E(Φ, ν) is calculated and shown to have an absolute minimum which corresponds to one flux quantum per particle. This optimal flux phenomenon is shown to occur under large conditions and for different lattices. An explicit cusp-like behavior of E νs. Φ at fixed ν is found both for the absolute and for the relative minima of E. Furthermore, the ground state energy is shown to be a smooth function of ν. The implications of our results for the stabilization of Anyons and the flux states are discussed.
The authors calculate the ground state energies and wavefunctions for small systems of fermions on a lattice using singly and doubly periodic boundary conditions. They find minima in the ground state energy when the magnetic flux per plaquette corresponds to filling fractions with odd denominators. They interpret these minima in terms of fractional quantum Hall states. The pair correlation function at nearest and next-nearest neighbours is calculated as a function of the repulsive interaction strength between particles.