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

TL;DR

This paper develops analytic equations of motion for matrix product states, enabling time evolution, response analysis, and Green function calculations, thus advancing the theoretical framework for simulating quantum many-body systems.

Contribution

It introduces a novel analytic approach to time evolution and response functions for MPS, including a random phase approximation and Green function analysis.

Findings

Derived equations of motion for MPS from the least action principle.

Established a matrix product state RPA for response and excitations.

Analyzed the structure of site-based Green functions and correlations.

Abstract

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.