Two-electron wavefunctions are matrix product states with bond dimension Three

TL;DR

This paper proves that for two-electron systems, the QC-DMRG method with bond dimension three, combined with fermionic mode optimization, exactly recovers the full configuration interaction (FCI) energy, establishing an optimal representation.

Contribution

The paper demonstrates that two-electron wavefunctions can be exactly represented as matrix product states with bond dimension three, proving optimality for the QC-DMRG approach.

Findings

QC-DMRG with bond dimension three recovers FCI energy for two-electron systems

Optimality of bond dimension three for two-electron wavefunctions

Wavefunctions can be exactly expressed as matrix product states with minimal bond dimension

Abstract

We prove the statement in the title, for a suitable (wavefunction-dependent) choice of the underlying orbitals, and show that Three is optimal. Thus for two-electron systems, the QC-DMRG method with bond dimension Three combined with fermionic mode optimization exactly recovers the FCI energy.