Phase transitions in the Hubbard Hamiltonian

Abstract

The authors study phase transitions in the isotropic non-degenerate Hubbard Hamiltonian with renormalization group techniques using the epsilon =4-d expansion to first order in epsilon . The functional obtained from the Hubbard Hamiltonian displays full rotational symmetry and describes two coupled fields: a vector spin field, with n components and a non-soft scalar charge field. This coupling is pure imaginary, which has interesting consequences for the critical properties of this coupled field system. The effect of simple constraints imposed on the charge field is considered. The relevance of the coupling between the fields in producing Fisher renormalisation of the critical exponents is discussed. The possible singularities introduced in the charge-charge correlation function by the coupling are also discussed.