Post-Matrix Product State Methods: To tangent space and beyond

TL;DR

This paper develops a detailed formalism for tangent states in matrix product states, enabling advanced analysis of time-evolution, excitations, and spectral functions, especially for translation-invariant systems.

Contribution

It introduces a comprehensive tangent space formalism for matrix product states and explores extensions beyond tangent space, advancing the theoretical framework for variational methods.

Findings

Formalism of tangent states detailed and applied to time-evolution

New illustrative results for translation-invariant systems

Discussion of extensions beyond tangent space

Abstract

We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time-evolution, excitations and spectral functions. We focus on the case of systems with translation invariance in the thermodynamic limit, where momentum is a well defined quantum number. We present some new illustrative results and discuss analogous constructions for other variational classes. We also discuss generalizations and extensions beyond the tangent space, and give a general outlook towards post matrix product methods.