We study the spin-exchange scattering amplitude at two-loop (1/
N2) order for the infinite-U Hubbard model away from the metal-insulator filling, with finite electron charge, for which a well-defined 1/N expansion is possible, the mean-field level being equivalent to Gutzwiller enhanced quasiparticles. We find a positive spin-exchange Landau parameter which suggests that the spin-density fluctuations show a well-defined collective mode near the metal-insulator filling. This behavior is interpreted as paralleling the spin and charge separation in the Luttinger liquid.
We investigate the ground state properties of the two-dimensional half-filled one band Hubbard model in the strong (large-
U) to intermediate coupling limit (i.e., away from the strict Heisenberg limit) using an effective spin-only low-energy theory that includes nearest-neighbor exchange, ring exchange, and all other spin interactions to order
t(t∕U)3. We show that the operator for the staggered magnetization, transformed for use in the effective theory, differs from that for the order parameter of the spin model by a renormalization factor accounting for the increased charge fluctuations as
t∕U is increased from the $t∕U\ensuremath{\rightarrow}0$ Heisenberg limit. These charge fluctuations lead to an increase of the quantum fluctuations over and above those for an
S=1∕2 antiferromagnet. The renormalization factor ensures that the zero temperature staggered moment for the Hubbard model is a monotonously decreasing function of
t∕U, despite the fact that the moment of the spin Hamiltonian, which depends on transverse spin fluctuations only, in an increasing function of
t∕U. We also comment on quantitative aspects of the
t∕U and
1∕S expansions.
The auxiliary boson method and 1/N expansion are applied to the solution of the Hubbard model in the U =
∞ limit, in functional integral form. The zero order term in the expansion gives the mean-field result of non-interacting enhanced mass quasiparticles, and the next order gives Gaussian fluctuations around the mean-field value, representing effective interactions between the quasiparticles. From the density-density correlation function, the collective mode indicates a very different behavior away from and close to half filling. The superconducting instability is examined to 1/$N\sp2$ order from the dominant double collective mode exchange. For a parabolic band, there is a p-wave triplet instability. But for a 2D square lattice, there is no superconducting pairing to this order. The effects of disorder on this system are also investigated. For moderate filling, the specific heat and scattering rate have the same results as predicted in the weakly interacting theories. Close to half-filling, the specific heat and scattering rate show a much sharper temperature and energy dependence.
Quantum Monte Carlo simulations are used to explore the phase diagram of the negative-U Hubbard model. As the system is doped away from half filling, 〈n〉=1, the s-wave pair-field correlations are enhanced and the charge-density-wave correlations suppressed. There is no indication of phase separation. Away from half filling, the pair-field correlations are consistent with Kosterlitz-Thouless scaling and a finite
Tc which peaks near 〈n〉=1 but vanishes at exactly half filling.
We study contributions to the spin-exchange scattering amplitude at two-loop (1/
N2) order for the metallic phase of the two-dimensional t-J model, for which a well-defined 1/N expansion is possible. We find for small hole dopings and small exchange couplings (t\ensuremath{\gg}J) a positive spin-exchange Landau parameter, which suggests that the spin-density fluctuations show a well-defined collective mode near the metal-insulator filling. This behavior results from the fact that the chirality fluctuations decouple from and are suppressed relative to the charge fluctuations for large mass enhancements. The result is interpreted as paralleling the collective spin and charge modes characteristic of the Luttinger liquid for low wave vectors.
Around a metal-to-insulator transition driven by repulsive interaction (Mott transition) the single-particle excitations and the collective excitations are equally important. Here we present results for the generic susceptibilities at zero temperature in the half-filled Hubbard model in infinite dimensions. Profiting from the high resolution of dynamic density-matrix renormalization at all energies, results for the charge, spin, and Cooper-pair susceptibilities in the metallic and the insulating phase are computed. In the insulating phase, an almost saturated local magnetic moment appears. In the metallic phase a pronounced low-energy peak is found in the spin response. It is the precursor of the magnetic moment in the insulator.