# Sharing Singlets: Exploring Valence Bond Solid States

• mavipranav
In summary, the conversation discusses the concept of singlet states and their sharing in a chain of spins. It is mentioned that for a chain of S = 1 spins, adjacent bonds can all be in a singlet state, but not for |S| = 1/2. The explanation for this is derived from the AKLT hamiltonian and the ground state is best understood using the Schwinger boson formalism.
mavipranav
Hello

I have come across this inexplicable fact mentioned in somewhere that for a chain of S = 1 spins, the adjacent bonds can all be in a singlet state i.e. singlets can be shared in this case (forming valence bond solids) but not, for example, for |S| = 1/2, the latter point being clear. I do not understand how singlets can be shared. Can someone mention what the shared-wavefunction across 3 sites looks like?

Thanks,
Mavi

The answer comes from the AKLT hamiltonian, wherein at each site, the spin 1 is decomposed into 2 spin-1'2's. This is the ground state of the said hamiltonian and can be best understood within the Schwinger boson formalism.

## What is a valence bond solid state?

A valence bond solid state is a type of solid state found in certain materials where the electrons are not free to move around. Instead, they are paired up and bonded to each other, creating a stable lattice structure.

## What is the significance of valence bond solid states?

Valence bond solid states play an important role in understanding the properties and behavior of materials, such as superconductors and magnetic materials. They also help explain the behavior of certain chemical reactions and the formation of molecules.

## How are valence bond solid states different from other types of solid states?

Unlike other types of solid states, such as metals or semiconductors, valence bond solid states do not have free electrons that can conduct electricity. Instead, the electrons are localized and bonded to each other, resulting in different properties and behaviors.

## What techniques are used to study valence bond solid states?

Scientists use a variety of techniques to study valence bond solid states, including X-ray diffraction, nuclear magnetic resonance, and electron spin resonance. These techniques allow researchers to examine the structure and properties of these materials at the atomic and molecular level.

## What real-world applications can come from studying valence bond solid states?

Understanding valence bond solid states can lead to the development of new materials and technologies, such as improved superconductors and more efficient batteries. It can also help in the design of new drugs and understanding of chemical reactions.

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