Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite basis limit

TL;DR

This paper presents an exact matrix product state representation for fully correlated electronic wavefunctions as the basis approaches completeness, demonstrating convergence through numerical DMRG calculations of C2 ground state.

Contribution

It introduces an exact MPS representation for correlated wavefunctions in the infinite basis limit, advancing the understanding of wavefunction convergence.

Findings

Exact MPS representation as basis approaches completeness

Numerical demonstration of convergence in C2 ground state

Use of DMRG to analyze core-valence entanglement

Abstract

In this article we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The complete basis limit is illustrated numerically using the density matrix renormalization group method by computing the core-valence entanglement in the C$_2$ ground state in increasing subsets of cc-pVTZ and pVQZ bases until convergence is reached.