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Transport and Spectra in the Half-filled Hubbard Model: A Dynamical Mean Field Study

We study the issues of scaling and universality in spectral and transport properties of the infinite dimensional particle--hole symmetric (half-filled) Hubbard model within dynamical mean field theory. One of the simplest and extensively used impurity solvers, namely the iterated perturbation theory approach is reformulated to avoid problems such as analytic continuation of Matsubara frequency quantities or calculating multi-dimensional integrals, while taking full account of the very sharp structures in the Green's functions that arise close to the Mott transitions and in the Mott insulator regime. We demonstrate its viability for the half-filled Hubbard model. Previous known results are reproduced within the present approach. The universal behavior of the spectral functions in the Fermi liquid regime is emphasized, and adiabatic continuity to the non-interacting limit is demonstrated. The dc resistivity in the metallic regime is known to be a non-monotonic function of temperature with a `coherence peak'. This feature is shown to be a universal feature occurring at a temperature roughly equal to the low energy scale of the system. A comparison to pressure dependent dc resistivity experiments on Selenium doped NiS$_2$ yields qualitatively good agreement. Resistivity hysteresis across the Mott transition is shown to be described qualitatively within the present framework. A direct comparison of the thermal hysteresis observed in V$_2$O$_3$ with our theoretical results yields a value of the hopping integral, which we find to be in the range estimated through first-principle methods. Finally, a systematic study of optical conductivity is carried out and the changes in absorption as a result of varying interaction strength and temperature are identified.