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Valence Bond Theory

Valence Bond Theory

Overview of Valence Bond Theory

Valence Bond Theory

Valence Bond Theory

Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...

Valence Bond Theory and Hybridized Orbitals

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According to valence bond theory, a covalent bond results when: (1) an orbital on one atom overlaps an orbital on a second atom, and (2) the single electrons in each orbital combine to form an electron pair. The strength of a covalent bond depends on the extent of overlap of the orbitals involved. Maximum overlap is possible when the orbitals overlap on a direct line between the two nuclei.
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Hybridization of Atomic Orbitals I

Hybridization of Atomic Orbitals I

The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...

Entropy and Solvation

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The process of surrounding a solute with solvent is called solvation. It involves evenly distributing the solute within the solvent. The rule of thumb for determining a solvent for a given compound is that like dissolves like. A good solvent has molecular characteristics similar to those of the compound to be dissolved. For example, polar solutions dissolve polar solutes, and apolar solvents dissolve apolar solutes. A polar solvent is a solvent that has a high dielectric constant (ϵ ≥ 15); an...

Bond Dissociation Energy and Activation Energy

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Bond energy is the energy required to break a bond homolytically. These values are usually expressed in units of kcal/mol or kJ/mol and are referred to as bond dissociation energies when given for specific bonds or average bond energies when indicated for a given type of bond over many compounds. Firstly, the bond dissociation energy for a single bond is weaker than that of a double bond, which in turn is weaker than that of a triple bond. Secondly, hydrogen forms relatively strong bonds with...

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A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

A Photonic System for Generating Unconditional Polarization-Entangled Photons Based on Multiple Quantum Interference

Published on: September 5, 2019

Valence bond entanglement entropy.

Fabien Alet¹, Sylvain Capponi, Nicolas Laflorencie

¹Laboratoire de Physique Théorique, IRSAMC, Université Paul Sabatier, CNRS, 31062 Toulouse, France. alet@irsamc.ups-tlse.fr

Physical Review Letters

|October 13, 2007

Summary

This summary is machine-generated.

We introduce valence bond entanglement entropy for quantum spin systems. This new measure, calculable via quantum Monte Carlo simulations, mirrors entanglement entropy in 1D and reveals area laws in 2D antiferromagnetic models.

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Area of Science:

Quantum physics
Condensed matter physics
Quantum information theory

Background:

Entanglement entropy quantifies quantum correlations in many-body systems.
Valence bond states are crucial in understanding quantum magnetism.
Calculating entanglement in complex quantum systems remains a challenge.

Purpose of the Study:

Introduce valence bond entanglement entropy for SU(2) quantum spin systems.
Develop a method to calculate this entropy using quantum Monte Carlo simulations.
Compare the behavior of valence bond entanglement entropy with von Neumann entanglement entropy.

Main Methods:

Definition of valence bond entanglement entropy as a count of shared spin singlets.
Application of quantum Monte Carlo simulations in the valence bond basis.
Numerical analysis of one-dimensional and two-dimensional quantum spin models.

Main Results:

Valence bond entanglement entropy successfully mimics von Neumann entanglement entropy in 1D systems.
A strict area law is observed for valence bond solid states in 2D.
Multiplicative logarithmic corrections are found for the Néel phase in 2D Heisenberg models.

Conclusions:

Valence bond entanglement entropy provides a viable and computable measure of entanglement in quantum spin systems.
The results highlight distinct entanglement scaling behaviors in different phases of 2D quantum magnets.
This work offers new insights into the characterization of quantum phases through entanglement measures.