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The adiabatic transport properties of U(1) invariant systems are determinedby the dependence of the ground state energy on the twisted boundary condition.We examine a one-dimensional tight-binding model in the presence of a singledefect and find that the ground state energy of the model shows a universaldependence on the twist angle that can be fully characterized by thetransmission coefficient of the scattering by the defect. We identify resultingpathological behaviors of Drude weights in the large system size limit: (i)both the linear and nonlinear Drude weights depend on the twist angle and (ii)the $N$-th order Drude weight diverges proportionally to the $(N-1)$-th powerof the system size. To clarify the physical implication of the divergence, wesimulate the real-time dynamics of the tight-binding model under a staticelectric field and show that the divergence does not necessarily imply thelarge current. Furthermore, we address the relation between our results and theboundary conformal field theory.

Adiabatic transport in one-dimensional systems with a single defect