High-order entropy measures and spin-free quantum entanglement for molecular problems

Abstract

A new entropy measure is proposed for the molecular electronic structure theory. The corresponding many-electron, Shannon-like measure reflects quantum entanglement between electronic subsystems with different spins. The related Renyi entropy is introduced, and its connection with the previously considered collectivity analysis is discussed. Investigation of the second-order reduced density matrix (2-RDM) allows one to define an irreducible, size-consistent component of the 2-RDM entropy and to find the irreducible component of the 2-RDM squared norm. Specific computations on several small molecules are carried out at the full configuration interaction level, providing new insights into non-classical, long-range electron correlations and quantum entanglement in these systems. The local spin analysis and the spin-correlator analysis reveal nontrivial spin structure underlying the entangled states.

Keywords:

• Entropy measure
• Quantum entanglement
• Spin-free quantum chemistry
• Fock construction
• Spin correlators
• Dissociated states

Acknowledgements

The authors are grateful to Kim Gunnerson for comments on the manuscript. Financial support of the DOE Grant No. DE-FG02-05ER15755 is gratefully appreciated.