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

Understand

Drawing on similarities in Hartree-Fock theory and the theory of matrix product states (MPS), we explore extensions to time evolution, response theory, and Green functions.

• We derive analytic equations of motion for MPS from the least action principle, which describe optimal evolution in the small time-step limit.
• We further show how linearized equations of motion yield a MPS random phase approximation, from which one obtains response functions and excitations.
• Finally we analyze the structure of site-based Green functions associated with MPS, as well as the structure of correlations introduced via the fluctuation-dissipation theorem.