Role of symmetry in the interplay of T=0 quantum-phase transitions with unconventional T>0 transport properties in integrable quantum lattice systems

We show that a generalized charge SU(2) symmetry of the one-dimensional (1D) Hubbard model in an infinitesimal flux $\varphi$ generates half-filling states from metallic states which lead to a finite charge stiffness $D(T)$ at finite temperature $T$, whose $T$ dependence we study. Our results are of general nature for many integrable quantum lattice systems, reveal the microscopic mechanisms behind their exotic $T>0$ transport properties and the interplay with T=0 quantum-phase transitions, and contribute to the further understanding of the transport of charge in systems of interacting ultracold fermionic atoms in 1D optical lattices, quasi-1D compounds, and 1D nanostructures.