Repulsive vs. attractive Hubbard model: transport properties and spin-lattice relaxation rate

TL;DR

This study compares transport and magnetic properties of the repulsive and attractive Hubbard models in infinite dimensions, revealing complex temperature behaviors and particle-hole asymmetries through dynamical mean-field theory calculations.

Contribution

It provides a detailed analysis of the differences in transport and magnetic responses between the two Hubbard models using advanced numerical methods.

Findings

Attractive Hubbard model shows complex temperature dependence in transport properties.

Resistivity peaks above the MIR value in the strongly attractive case.

Spin-lattice relaxation rate exhibits non-monotonic behavior indicating pairing fluctuations.

Abstract

We contrast the transport properties (dc resistivity, Seebeck coefficient), optical conductivity, spectral functions, dynamical magnetic susceptibility, and the NMR $1/T_1$ spin-lattice relaxation rate of the repulsive and attractive infinite-dimensional Hubbard models in the paramagnetic phase for a generic band filling. The calculations are performed in a wide temperature interval using the dynamical mean-field theory with the numerical renormalization group as the impurity solver. The attractive case exhibits significantly more complex temperature dependences which can be explained by the behavior of the half-filled Hubbard model in external magnetic field with constant magnetization, to which the attractive Hubbard model maps through the partial particle-hole transformation. The resistivity is non-monotonous for strongly attractive case: it peaks significantly above the MIR value at a temperature $T_\mathrm{max}$ where the quasiparticle band disappears. For both signs of $U$ we find particle-hole asymmetry in the self-energy at low energies, but with the opposite kind of excitations having longer lifetime. This leads to a strong suppression of the slope of the Seebeck coefficient in the attractive case, rather than an enhancement as in the repulsive case. The spin-lattice relaxation rate in the strongly attractive case has a non-monotonic temperature dependence, thereby revealing the pairing fluctuations.