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Drawing on similarities in Hartree-Fock theory and the theory of matrixproduct states (MPS), we explore extensions to time evolution, response theory,and Green functions. We derive analytic equations of motion for MPS from theleast action principle, which describe optimal evolution in the small time-steplimit. We further show how linearized equations of motion yield a MPS randomphase approximation, from which one obtains response functions and excitations.Finally we analyze the structure of site-based Green functions associated withMPS, as well as the structure of correlations introduced via thefluctuation-dissipation theorem.

Analytic Time Evolution, Random Phase Approximation, and Green Functions for Matrix Product States