All Questions
5
questions
0
votes
1
answer
58
views
Showing that the ground state of the Heisenberg ferromagnet is an eigenstate of the Hamiltonian
The Hamiltonian of a Heisenberg ferromagnet in terms of $S^+, S^-, S^z$ is given by:
$$H = -\frac{1}{2}|J| \sum_{i,\vec{\delta}} \left[\frac{1}{2}(S_i^+S^-_{i+\vec{\delta}} + S_i^-S^+_{i+\vec{\delta}})...
- 665
3
votes
1
answer
92
views
Hamiltonians with collective quantum spins and their ground states
This feels like it could be a undergrad/grad-school quantum mechanics course level problem, or potentially something pretty interesting. I'd be happy with either answer, but I don't know which one is ...
- 368
0
votes
1
answer
4k
views
Ground state of the Heisenberg XXX model with a coupling?
I have a one-dimensional Heisenberg chain with a Magnetic field with $N$ sites with $J>0$
\begin{equation}
\mathcal{H} = -J \sum_{i = 1}^{N-1} \vec{S_i}\cdot \vec{S_{i+1}}- \sum_{i = 1}^N \vec{H}\...
- 904
2
votes
1
answer
187
views
Microscopic and macroscopic description of spin waves
Hamiltonian
Consider the one-dimensional Heisenberg ferromagnet specified by the Hamiltonian
$$H = -\frac{|J|}{2}\sum_{i,\delta} \mathbf{S}_i\cdot \mathbf{S}_{i+\delta}.$$
Here $i$ labels the spin ...
- 451
2
votes
0
answers
124
views
Can we have a spin glass in the one-dimensional Heisenberg hamiltonian with nearest neighbours only?
Consider the one dimensional Heisenberg Hamiltonian of the form
\begin{equation}
H = - \sum_{<i,j>} J_{ij} \mathbf{S}_i \cdot \mathbf{S}_j
\end{equation}
with nearest neighbour interactions. ...
- 451