Minimal matrix product states and generalizations of mean-field and geminal wavefunctions

Abstract

Simple wavefunctions of low computational cost but which can achieve qualitative accuracy across the whole potential energy surface (PES) are of relevance to many areas of electronic structure as well as to applications to dynamics. Here, we explore a class of simple wavefunctions, the minimal matrix product state (MMPS), that generalizes many simple wavefunctions in common use, such as projected mean-field wavefunctions, geminal wavefunctions, and generalized valence bond states. By examining the performance of MMPSs for PESs of some prototypical systems, we find that they yield good qualitative behavior across the whole PES, often significantly improving on the aforementioned ansätze.

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• Molecular Quantum Circuit Design: A Graph-Based Approach
• Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions
• 2500 vibronic eigenstates of the NO${}_3$ radical
• Benchmarking vibrational spectra: 5000 accurate eigenstates of acetonitrile using tree tensor network states
• Simulating real-time molecular electron dynamics efficiently using the time-dependent density matrix renormalization group
• Computing excited eigenstates using inexact Lanczos methods and tree tensor network states
• Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory
• Coupled-cluster pairing models for radicals with strong correlations
• Algebro-geometric approach to a fermion self-consistent field theory on coset space SU(m+n)/S(U(m) x U(n))