J. Stein

Unitary flow of the bosonized large-N Lipkin model

The flow equations describing the continuous unitary transformation which brings the Hamiltonian closer to diagonality are derived and solved exactly for the Lipkin model in the Holstein-Primakoff boson representation and for a large particle number N . The transformed Hamiltonian is diagonal in order 1/N 3 , extending known linear transformations to next-higher orders in the inverse particle number. This approach quite naturally allows one to preserve the tridiagonal structure of the original Lipkin Hamiltonian in the course of the transformation. Exact analytical results for the coupling functions and explicit expressions for the ground state energy and for the energy gap to the first excited state in order 1/N 2 are presented and are compared with the accurate numerical values.

Field theoretic treatment of the strong-coupling attractive Hubbard model with diagonal disorder

The authors present a field theoretic formulation of the strong-coupling attractive Hubbard model with Gaussian distributed random on-site energies. Self-consistency equations for the order parameters of superconductivity and charge ordering are derived at lowest loop order and solved for the limiting cases of weak and strong disorder. They also study dynamical properties and calculate the influence of disorder on the Bogoliubov-Anderson mode in the superconducting phase.

Superfluid density of the two-dimensional strong-coupling attractive Hubbard model

The low-temperature result for the superfluid density of the attractive (negative-U) Hubbard model in two dimensions and in the strong-coupling limit is obtained, applying a field-theoretic representation of the model and utilizing a hydrodynamic relation between the order parameter field, the correlation function for soft planar fluctuations, and the superfluid density. This microscopic derivation does not involve self-consistency arguments and allows one to include the influence of the out-of-plane pseudo-spin fluctuations which become singular at half band-filling and suppress a Kosterlitz-Thouless transition at finite temperature. The results is in good agreement with quantum Monte Carlo data.

One-loop result for the Bogoliubov-Anderson mode of the superconducting strong coupling attractive Hubbard model

Abstract We present the one-loop calculations for the sound-like Bogoliubov-Anderson mode in the superconducting phase of the attractive Hubbard model in the strong coupling limit. It is found that in the leading dimensional singularities and for low temperatures the zero-loop expression is modified only by a global correction factor; as a consequence the dispersion relation and the Bogoliubov velocity retain their zero-loop results.

Interacting fluctuations and the two-loop order parameters of the strong-coupling negative-U Hubbard model

The effective field theory that describes the interaction of fluctuations of the attractive Hubbard model in the strong-coupling limit is formulated and applied to obtain the two-loop results for the order parameters of the model at low temperatures and in the leading singularities near two dimensions. Starting from a Grassmann functional integral representation of the strong-coupling model on the restricted fermionic Hilbert space, which corresponds to the anisotropic spin-12 Heisenberg quantum antiferromagnet, we derive the effective field theory up to fifth order in the bosonic fluctuation fields. The loop corrections of the order parameters for superconductivity and charge ordering and of the chemical potential are evaluated including both the singular planar phase fluctuations and the out-of-plane fluctuations, which become soft at half band-filling. The results are in agreement with the scaling behaviour expected from the corresponding XY and Heisenberg limits of the O(n) non-linear σ-model.