We propose that spatial density matrices, which are singularly important in the study of quantum entanglement, encode the electronic fluctuations and correlations responsible for covalent bonding. From these density matrices, we develop tools that allow us to analyse how many body wave functions can be broken up into real space pieces. We apply these tools to the first row dimers, and in particular, we address the conflicting evidence in the literature about the presence of an inverted fourth bond and anti-ferromagnetic correlations in the $\text{C}_2$ molecule. Our results show that many body effects enhance anti-ferromagnetic fluctuations but are not related to the formation of an inverted fourth bond. We identify two inverted bonds in the $\text{C}_2$ molecule and establish their correspondence to the bonds in the $\text{Be}_2$ molecule. Additionally, we provide a new interpretation of the Mayer index, introduce partial bonds to fix deficiencies in molecular orbital theory, and prove the Hartree-Fock wave function for C $_{2}$ is not a triple bond. Our results suggest that entanglement-based methods can lead to a more realistic treatment of molecular and extended systems than possible before.We propose that spatial density matrices, which are singularly important in the study of quantum entanglement, encode the electronic fluctuations and correlations responsible for covalent bonding. From these density matrices, we develop tools that allow us to analyse how many body wave functions can be broken up into real space pieces. We apply these tools to the first row dimers, and in particular, we address the conflicting evidence in the literature about the presence of an inverted fourth bond and anti-ferromagnetic correlations in the $\text{C}_2$ molecule. Our results show that many body effects enhance anti-ferromagnetic fluctuations but are not related to the formation of an inverted fourth bond. We identify two inverted bonds in the $\text{C}_2$ molecule and establish their correspondence to the bonds in the $\text{Be}_2$ molecule. Additionally, we provide a new interpretation of the Mayer index, introduce partial bonds to fix deficiencies in molecular orbital theory, and prove the Hartree-Fock wave function for C$_{2}$ is not a triple bond. Our results suggest that entanglement-based methods can lead to a more realistic treatment of molecular and extended systems than possible before.

arXiv:1412.1495Dec 3, 20142 citations

Entanglement in Resonating Valence Bond states

Weifei Li, Tommaso Roscilde, Stephan Haas

Bulletin of the American Physical SocietyMar 21, 20050 citations

Calculating the entanglement spectrum in quantum Monte Carlo with application toab initioHamiltonians

Norm M. Tubman, David ChangMo Yang

Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order R\'enyi entropies and maximum entropy techniques. We present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix and we determine an estimator that can be used in variational Monte Carlo as well as other Monte Carlo methods. The algorithm is based on using a generalization of the swap operator, which can be extended to calculate a general class of density matrices that can include combinations of spin, space, particle, and even momentum degrees of freedom. We demonstrate the method by applying it to the ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ molecules and describe how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.Several algorithms have been proposed to calculate the spatial entanglement spectrum from high order R\'enyi entropies and maximum entropy techniques. We present an alternative approach for computing the entanglement spectrum with quantum Monte Carlo for both continuum and lattice Hamiltonians. This method provides direct access to the matrix elements of the spatially reduced density matrix and we determine an estimator that can be used in variational Monte Carlo as well as other Monte Carlo methods. The algorithm is based on using a generalization of the swap operator, which can be extended to calculate a general class of density matrices that can include combinations of spin, space, particle, and even momentum degrees of freedom. We demonstrate the method by applying it to the ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ molecules and describe how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.

arXiv:1402.0503Physical Review BAug 28, 201419 citations

Entanglement spectroscopy

Nicolas Regnault

May 1, 20130 citations

Entanglement of electrons in interacting molecules

Tina A. C. Maiolo, Fabio Della Sala, L. Martina +1 more

arXiv:quant-ph/0610238Theoretical and Mathematical PhysicsAug 1, 20078 citations

Exact entanglement correlation complementsthe chemical bond description

Józef Spałek, Maciej Hendzel, Piotr Kuterba

We analyze the properties of the exact solution obtained by us recently for the extended Heitler-London model of the chemical bonding in an analytic form. The emphasis, put on defining the two-particle entanglement correlation, and expressing it by the von Neumann entropy, which provides the complementary characterization of the chemical bond and is directly related to the partial atomicity and the true covalency. The newly introduced concepts refine the standard analysis of covalency based solely on the wave-function and related energy description of the bond as a pure state. We show that a gradual evolution of the system with the increasing interatomic distance of the indistinguishable two electrons composing the bond into their distinguishable correspondents in the atomic (dissociation) limit can be traced out systematically. In particular, only by taking into account the atomicity the true covalency vanishes in the latter limit.We analyze the properties of the exact solution obtained by us recently for the extended Heitler-London model of the chemical bonding in an analytic form. The emphasis, put on defining the two-particle entanglement correlation, and expressing it by the von Neumann entropy, which provides the complementary characterization of the chemical bond and is directly related to the partial atomicity and the true covalency. The newly introduced concepts refine the standard analysis of covalency based solely on the wave-function and related energy description of the bond as a pure state. We show that a gradual evolution of the system with the increasing interatomic distance of the indistinguishable two electrons composing the bond into their distinguishable correspondents in the atomic (dissociation) limit can be traced out systematically. In particular, only by taking into account the atomicity the true covalency vanishes in the latter limit.

Nov 21, 20241 citation

\text{C}_2

molecule. Our results show that many body effects enhance anti-ferromagnetic fluctuations but are not related to the formation of an inverted fourth bond. We identify two inverted bonds in the

\text{C}_2

molecule and establish their correspondence to the bonds in the

\text{Be}_2

molecule. Additionally, we provide a new interpretation of the Mayer index, introduce partial bonds to fix deficiencies in molecular orbital theory, and prove the Hartree-Fock wave function for C

_{2}

is not a triple bond. Our results suggest that entanglement-based methods can lead to a more realistic treatment of molecular and extended systems than possible before.

{\mathrm{H}}_{2}

and

{\mathrm{N}}_{2}

molecules and describe how the spatial entanglement spectrum encodes a covalent bond that includes all the many body correlations.