Adiabatic transport in one-dimensional systems with a single defect

TL;DR

This paper investigates how a single defect affects adiabatic transport in one-dimensional systems, revealing universal energy dependence on boundary twists and pathological behaviors of Drude weights, with implications for real-time dynamics and boundary theories.

Contribution

It demonstrates the universal dependence of ground state energy on boundary twists in defected 1D systems and uncovers divergence behaviors in Drude weights, linking them to physical transport properties.

Findings

Ground state energy depends universally on the twist angle via the defect's transmission coefficient.

Both linear and nonlinear Drude weights depend on the twist angle and diverge with system size.

Divergence of Drude weights does not necessarily lead to large currents in real-time dynamics.

Abstract

The adiabatic transport properties of U(1) invariant systems are determined by 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 single defect and find that the ground state energy of the model shows a universal dependence on the twist angle that can be fully characterized by the transmission coefficient of the scattering by the defect. We identify resulting pathological 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 power of the system size. To clarify the physical implication of the divergence, we simulate the real-time dynamics of the tight-binding model under a static electric field and show that the divergence does not necessarily imply the large current. Furthermore, we address the relation between our results and the boundary conformal field theory.