Large Cumulant Eigenvalue as a Signature of Exciton Condensation

TL;DR

This paper introduces a new computational method using the large eigenvalue of the cumulant part of the particle-hole reduced density matrix to predict exciton condensation, applicable to molecules and materials.

Contribution

It demonstrates that a large eigenvalue in the cumulant matrix uniquely indicates exciton condensation, providing a size-extensive measure for the first time.

Findings

Large eigenvalue correlates with exciton condensation.

Method successfully predicts condensation in Lipkin model and benzene stacks.

Eigenvalue bounded by the number of excitons in the thermodynamic limit.

Abstract

The Bose-Einstein condensation of excitons into a single quantum state is known as exciton condensation. Exciton condensation, which potentially supports the frictionless flow of energy, has recently been realized in graphene bilayers and van der Waals heterostructures. Here we show that exciton condensates can be predicted from a combination of reduced density matrix theory and cumulant theory. We show that exciton condensation occurs if and only if there exists a large eigenvalue in the cumulant part of the particle-hole reduced density matrix. In the thermodynamic limit we show that the large eigenvalue is bounded from above by the number of excitons. In contrast to the eigenvalues of the particle-hole matrix, the large eigenvalue of the cumulant matrix has the advantage of providing a size-extensive measure of the extent of condensation. Here we apply this signature to predict exciton condensation in both the Lipkin model and molecular stacks of benzene. The computational signature has applications to the prediction of exciton condensation in both molecules and materials.