  Subsystems of strongly disordered, interacting quantum systems can fail to
thermalize because of the phenomenon of many-body localization (MBL). In this
article, we explore a tensor network description of the eigenspectra of such
systems. Specifically, we will argue that the presence of a complete set of
local integrals of motion in MBL implies an efficient representation of the
entire spectrum of energy eigenstates with a single tensor network, a
\emph{spectral} tensor network. Our results are rigorous for a class of
idealized systems related to MBL with integrals of motion of finite support. In
one spatial dimension, the spectral tensor network allows for the efficient
computation of expectation values of a large class of operators (including
local operators and string operators) in individual energy eigenstates and in
ensembles.
