Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2007-03-21
Pramana68:819,2007
Physics
Condensed Matter
Strongly Correlated Electrons
A shorter version of this paper will appear in Pramana - Journal of Physics
Scientific paper
10.1007/s12043-007-0080-y
We use different types of determinantal Hartree-Fock (HF) wave functions to calculate variational bounds for the ground state energy of spin-half fermions in volume V_0, with mass m, electric charge zero, and magnetic moment mu, which are interacting through long range magnetic dipole-dipole interaction. We find that at high densities when the average inter particle distance r_0 becomes small compared to the magnetic length r_m, a ferromagnetic state with spheroidal occupation function, involving quadrupolar deformation, gives a lower energy compared to the variational energy for the uniform paramagnetic state. This HF variational bound to the ground state energy turns out to have a lower energy than our earlier calculation in which instead of a determinantal wavefunction we had used a positive semi-definite single particle density matrix operator whose eigenvalues, having quadrupolar deformation, were allowed to take any value from 0 to 1. This system is of course still unstable towards infinite density collapse, but we show here explicitly that a suitable short range repulsive (hard core) interaction of strength U_0 and range a can stop this collapse.The existence of a stable high density ferromagnetic state with spheroidal occupation function is possible as long as the ratio of hard-core and magnetic dipole coupling constants is not very small compared to 1.
Jha Sudhanshu S.
Mahanti S. D.
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