  A tensor is a multi-dimensional array of complex numbers, and the Lohe tensor
model is an aggregation model on the space of tensors with the same rank and
size. It incorporates previously well-studied aggregation models on the space
of low-rank tensors such as the Kuramoto model, Lohe sphere and matrix models
as special cases. Due to its structural complexities in cubic interactions for
the Lohe tensor model, explicit construction of solutions with specific
structures looks daunting. Recently, we obtained completely separable states by
associating rank-1 tensors. In this paper, we further investigate another type
of solutions, namely "{\it quadratically separable states}" consisting of
tensor products of matrices and their component rank-2 tensors are solutions to
the double matrix model whose emergent dynamics can be studied using the same
methodology of the Lohe matrix model.
