Decay properties of the density matrix and Wannier functions for interacting systems

TL;DR

This paper extends the concept of exponential decay of the density matrix and Wannier functions from non-interacting to interacting systems, providing a new way to characterize insulators including Mott insulators.

Contribution

It introduces many-body Wannier functions and demonstrates their decay properties, bridging the gap between non-interacting and interacting electron systems.

Findings

Exponential decay characterizes both band and Mott insulators.

Many-body Wannier functions differ from non-interacting Wannier functions.

Decay properties can classify insulating states in interacting systems.

Abstract

For non-interacting electrons the one-particle density matrix and the related Wannier functions characterize a material as insulating or metallic. Introducing many-body Wannier functions, we show that this characterization can be carried over to interacting systems. In particular, we find that an exponential decay of the density matrix characterizes not only band insulators but also Mott insulators. The properties of the many-body Wannier functions differ, however, from those of the Wannier functions of a non-interacting systems.