Interplay of magnetism and temperature in the large-demensional limits of the Hubbard and t-J models

We describe a theory for the finite-temperature properties of the infinite dimensional (d∞) half-filled Hubbard model and the t-J model. The work presented extends the local moment approach (LMA) to include the effects of temperature. We start by investigating the t-J model, which provides the leading strong coupling asymptotics to the Hubbard model. The only relevant energy scale, apart from temperature T, is the cost to flip a spin in the exchange field of the neighbouring spins. By identifying the temperature dependence of the spin-flip cost wp, we are able to obtain an exact solution to the d∞ t-J model. For the Hubbard model we first consider a scenario where T enters solely implicitly via the thermal disorder of the local moment state, which we describe at unrestricted Hartree-Fock level. The low-energy scale for spin-flip excitations is identified via an RPA treatment of the transverse spin polarization propagator. Dynamical coupling of single-particle processes to the spin-excitations yields a renormalized self-consistent description of the self-energy. This is shown to be asymptotically exact in strong coupling and results describing the thermal evolution of the spectra are discussed for moderate to strong Interaction strengths. By translating the diagrams for the RPA-propagator and the self-energy into the imaginary-frequency formalism we include explicit temperature effects via Fermi functions. The imaginary-frequency expressions are then analytically continued to obtain the related retarded real-frequency expressions. We also derive the correct form of the dynamical conductivity on the d∞ Bethe lattice. Results for finite-temperature single-particle spectra and conductivities are then presented and particular attention given to the thermal evolution of these quantities and the finite-temperature insulator to metal crossover. (author)