Efficient evaluation of AGP reduced density matrices

Abstract

We propose and implement an algorithm to calculate the norm and reduced density matrices of the antisymmetrized geminal power (AGP) of any rank with polynomial cost. Our method scales quadratically per element of the reduced density matrices. Numerical tests indicate that our method is very fast and capable of treating systems with a few thousand orbitals and hundreds of electrons reliably in double-precision. In addition, we present reconstruction formulae that allows one to decompose higher order reduced density matrices in terms of linear combinations of lower order ones, thereby reducing the computational cost significantly.

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• Density Matrices of Seniority-Zero Geminal Wavefunctions
• Wave function methods for canonical ensemble thermal averages in correlated many-fermion systems
• Construction of linearly independent non-orthogonal AGP states
• Reduced Density Matrices / Static Correlation Functions of Richardson-Gaudin States Without Rapidities
• AGP-based unitary coupled cluster theory for quantum computers
• Robust formulation of Wick's theorem for computing matrix elements between Hartree-Fock-Bogoliubov wavefunctions
• Confirming the role of nuclear tunnelling in aqueous ferrous-ferric electron transfer
• Exploring Spin AGP Ansatze for Strongly Correlated Spin Systems
• A Pseudo-BCS Wavefunction from Density Matrix Decomposition:Application in Auxiliary-Field Quantum Monte Carlo
• State preparation of AGP on a quantum computer without number projection
• Variational theory combining number-projected BCS and coupled-cluster doubles
• Accurate and precise quantum computation of valence two-neutron systems
• Correlated pair ansatz with a binary tree structure
• Near-exact treatment of seniority-zero ground and excited states with a Richardson-Gaudin mean-field
• Symmetry-Projected Spin-AGP Methods Applied to Spin Systems
• Transition density matrices of Richardson-Gaudin states
• Bootstrapping Flat-band Superconductors: Rigorous Lower Bounds on Superfluid Stiffness