Two dimenstional Heisenberg Hamiltonian for spin 1/2 system

In summary, the Two Dimensional Heisenberg Hamiltonian is a mathematical representation of interactions between spin 1/2 particles in a two-dimensional lattice. It is derived from the principles of quantum mechanics and the Heisenberg model and makes assumptions about the particles' spin, isotropic interactions, and absence of external magnetic fields. This Hamiltonian has various applications in the study of magnetic materials and differs from the one-dimensional and three-dimensional versions in the number of dimensions it considers.
  • #1
Noora Alameri
12
0
Hey everybody,

I am trying to expand a system of seven qubits from one dimensional Hamiltonian to the two dimensional representation.

I have the one dimensional representation and I don't know what to add to transform it from 1D to 2D representation.

I would really appreciate your help and guidance.

Here is my !D Hamiltonian:

152157332685491.png
Thank You,
Noora
 

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  • #2
How are the cubits arranged in 2D?
 

Related to Two dimenstional Heisenberg Hamiltonian for spin 1/2 system

1. What is the Two Dimensional Heisenberg Hamiltonian for spin 1/2 system?

The Two Dimensional Heisenberg Hamiltonian for spin 1/2 system is a mathematical representation of the interactions between spin 1/2 particles in a two dimensional lattice. It takes into account the exchange interactions between neighboring particles and can be used to study the behavior of magnetic materials in two dimensions.

2. How is the Two Dimensional Heisenberg Hamiltonian derived?

The Two Dimensional Heisenberg Hamiltonian is derived from the principles of quantum mechanics and the Heisenberg model, which describes the interactions between magnetic moments in a material. It is a simplified version of the three-dimensional Hamiltonian and is often used in studies of thin films and other two-dimensional systems.

3. What are the key assumptions made in the Two Dimensional Heisenberg Hamiltonian?

The Two Dimensional Heisenberg Hamiltonian assumes that the particles in the system have spin 1/2 and that they interact through exchange interactions. It also assumes that the interactions are isotropic, meaning they are the same in all directions, and that there is no external magnetic field present.

4. What are the main applications of the Two Dimensional Heisenberg Hamiltonian?

The Two Dimensional Heisenberg Hamiltonian has many applications in the study of magnetic materials, including thin films, nanoscale systems, and magnetic nanoparticles. It is also used in fields such as quantum computing and spintronics, which utilize the properties of spin for information processing and storage.

5. How does the Two Dimensional Heisenberg Hamiltonian differ from the one-dimensional and three-dimensional versions?

The Two Dimensional Heisenberg Hamiltonian differs from the one-dimensional and three-dimensional versions in the number of dimensions it considers. The one-dimensional version only takes into account interactions along a line, while the three-dimensional version includes interactions in all three dimensions. The two-dimensional version takes into account interactions in a plane, but not in the third dimension.

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