Drude weight in systems with open boundary conditions

For finite systems, the real part of the conductivity is usually decomposed as the sum of a zero frequency delta peak and a finite frequency regular part. In studies with periodic boundary conditions, the Drude weight, i.e., the weight of the zero frequency delta peak, is found to be nonzero for integrable systems, even at very high temperatures, whereas it vanishes for generic nonintegrable systems. Paradoxically, for systems with open boundary conditions, it can be shown that the coefficient of the zero frequency delta peak is identically zero for any finite system, regardless of its integrability. In order for the Drude weight to be a thermodynamically meaningful quantity, both kinds of boundary conditions should produce the same answer in the thermodynamic limit. We shed light on these issues by using analytical and numerical methods.