Drude weight in systems with open boundary conditions

TL;DR

This paper investigates how boundary conditions affect the Drude weight in finite systems, revealing that open boundaries lead to a zero Drude weight regardless of integrability, contrasting with periodic systems.

Contribution

The study clarifies the discrepancy between boundary conditions by combining analytical and numerical methods to understand the thermodynamic limit behavior of the Drude weight.

Findings

Open boundary conditions yield zero Drude weight for finite systems.

Periodic boundary conditions show nonzero Drude weight in integrable systems.

The results reconcile differences in Drude weight behavior across boundary conditions.

Abstract

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.