Validity of finite-window evolution in the compressed regime

Characterize the accuracy and dynamics of the LOMPS algorithm in the compressed regime, where the variational manifold has fewer physical parameters than the space of generic translation-invariant L-site reduced density matrices and therefore cannot generally represent the target exactly.

Background

The LOMPS algorithm represents local reduced density matrices using a one-site translation-invariant uniform matrix-product-state manifold. A parameter-counting condition distinguishes a locally expressive regime, in which the MPS manifold has at least as many physical parameters as a generic L-site reduced density matrix, from a compressed regime, in which it has fewer parameters.

In the compressed regime, generic local reduced density matrices cannot be represented exactly, so the projection cost includes an intrinsic representation error in addition to the finite-window error. The paper notes that this regime could substantially reduce computational resources, but does not establish how the resulting representation error affects the accuracy or dynamics of LOMPS trajectories.