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.

References in corpus (37)

• The density-matrix renormalization group in the age of matrix product states
• Global Optimization by Basin-Hopping and the Lowest Energy Structures of Lennard-Jones Clusters Containing up to 110 Atoms
• Recent developments in the PySCF program package
• Ab Initio Quantum Chemistry using the Density Matrix Renormalization Group
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• A spin-adapted Density Matrix Renormalization Group algorithm for quantum chemistry
• Density matrix renormalization group algorithms with a single center site
• Correlated geminal wave function for molecules: an efficient resonating valence bond approach
• Quantum information analysis of electronic states at different molecular structures
• Geminal wavefunctions with Jastrow correlation: a first application to atoms
• An Efficient Matrix Product Operator Representation of the Quantum-Chemical Hamiltonian
• N-electron valence state perturbation theory based on a density matrix renormalization group reference function, with applications to the chromium dimer and poly-p-phenylene vinylene oligomer
• Projected Quasiparticle Theory for Molecular Electronic Structure
• Variational quantum Monte Carlo simulations with tensor-network states
• Multiconfigurational time-dependent Hartree approaches for indistinguishable particles
• Density-matrix renormalization-group method in momentum space
• A general second order complete active space self-consistent-field solver for large-scale systems
• Multi-reference perturbation theory with Cholesky decomposition for the density matrix renormalization group
• Optimizing large parameter sets in variational quantum Monte Carlo
• Density Matrix Renormalization Group with Efficient Dynamical Electron Correlation Through Range Separation
• Symmetry-Projected Hartree-Fock-Bogoliubov Equations
• Spin-adapted Matrix Product States and Operators
• Electronic landscape of the P-cluster of nitrogenase as revealed through many-electron quantum wavefunctions
• An exactly size consistent geminal power via Jastrow factor networks in a local one particle basis
• Efficient Formulation of Full Configuration Interaction Quantum Monte Carlo in a Spin Eigenbasis via the Graphical Unitary Group Approach
• Calculating vibrational spectra with sum of product basis functions without storing full-dimensional vectors or matrices
• Computing vibrational eigenstates with tree tensor network states (TTNS)
• Targeted Excited State Algorithms
• Linear Response Theory for the Density Matrix Renormalization Group: Efficient Algorithms for Strongly Correlated Excited States
• Optimization of highly excited matrix product states with an application to vibrational spectroscopy
• Projected Hartree Fock Theory as a Polynomial Similarity Transformation Theory of Single Excitations
• Projected Hartree-Fock as a Polynomial of Particle-Hole Excitations and Its Combination With Variational Coupled Cluster Theory
• Symmetry projected Jastrow mean field wavefunction in variational Monte Carlo
• An efficient stochastic algorithm for the perturbative density matrix renormalization group in large active spaces
• The multi-configurational time-dependent Hartree approach in optimized second quantization: imaginary time propagation and particle number conservation
• On construction of projection operators

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• Connections between Richardson-Gaudin States, Perfect-Pairing, and Pair Coupled-Cluster Theory
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