# Define spin operators for numerical groundstate obtained by ED

• A
• woodydewer
In summary, the conversation discusses the topic of measuring spin components of ground states obtained by ED. The speaker is seeking a way to define spin operators for their code and mentions trying to rewrite as a correlation function or with the partition sum. The other person suggests that the post may receive a good answer, but notes that the question may not be clear to those who do not have prior knowledge. The original speaker then states that they have solved the problem.
woodydewer
TL;DR Summary
The ground state obtained by ED is not in a suitable representation and I am looking for a way to define spin operators working with that.
Hi,
I want to measure spin components of a ground state of some models. These ground states are obtained by ED. The states for constructing the Hamiltonian are integers representing spins in binary. As the ground state (and the other eigenvectors) are now not anymore in a suitable representation (just vectors with doubles as components instead of integers), I am looking for a way to define my spin operators to measure the components suitable for my code.

I tried rewriting as Correlation function or with the partition sum. Do you have any ideas?

It's possible that your post may get a good answer. What you are asking, however, may not be clear to anyone who does not already know precisely what you are trying to do.

woodydewer
Hi, I could solve it. :)

## 1. What are spin operators?

Spin operators are mathematical operators used in quantum mechanics to describe the spin of a particle. They are represented by matrices and are used to calculate the spin of a particle in a given state.

## 2. How are spin operators defined?

Spin operators are defined as matrices that operate on the wavefunction of a particle to determine its spin. In quantum mechanics, spin operators are represented by the Pauli matrices or the more general spin matrices.

## 3. What is the significance of spin operators in numerical groundstate calculations?

Spin operators are crucial in numerical groundstate calculations because they allow us to determine the spin of a particle in a given state. This information is essential for understanding the behavior of particles in quantum systems and for predicting their properties.

## 4. How are spin operators used in exact diagonalization (ED)?

In exact diagonalization, spin operators are used to calculate the spin of a particle in a given state. They are incorporated into the Hamiltonian matrix, which is then diagonalized to obtain the groundstate energy and wavefunction of the system.

## 5. Are spin operators only applicable to spin-1/2 particles?

No, spin operators can be used for particles with any spin value. However, they are most commonly used for spin-1/2 particles because they can be represented by the Pauli matrices, which are easier to work with mathematically.

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