  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.
