All Questions
Tagged with spin-models quantum-spin
39
questions with no upvoted or accepted answers
4
votes
0
answers
141
views
Energy gap of a Heisenberg model on bipartite lattices
Consider the antiferromagnetic Heisenberg model on some "graph" where each vertex corresponds to a spin-1/2 and the edges represent interaction between the vertices, i.e.,
\begin{equation}
\...
- 321
4
votes
0
answers
89
views
Operator inequality between the Heisenberg Hamiltonian and the total spin
Consider a collection of $N$ spin-1/2 particles (qubits) with total spin
$$\vec{S} = \frac{1}{2}\sum_{n=1}^N \vec{\sigma}_n$$
and a Heisenberg Hamiltonian
$$H = -J \sum_{\langle n,m\rangle} \vec{\...
- 3,684
4
votes
0
answers
599
views
What is the relation between the Holstein-Primakoff Transformation and Bethe's Ansatz for the Heisenberg Ferromagnet?
Bethe's Ansatz is a method to find the eigenenergies and eigenstates of the Heisenberg ferromagnet (see also spin waves). For a general n-excitation state it involves solving rather complicated ...
- 11.6k
3
votes
0
answers
44
views
What $(2+0)d$ classical model becomes the $(1+1)d$ Heisenberg model?
The $(1+1)d$ transverse-field Ising chain is closely related to the $(2+0)d$ Ising model. In particular, the $(2+0)d$ classical Ising model has a transfer matrix that can be written suggestively as $e^...
- 2,292
3
votes
0
answers
419
views
Difference between 1D and 3D Heisenberg model
As is given in Wikipedia the $1$D Heisenberg model is:
$$ \hat{H} = -J\sum_{i=1}^N \sigma_i\sigma_{i+1} - h\sum_{i=1}^N \sigma_i $$
And the $3$D Heisenberg model is:
$$ \hat{H} = -\tfrac{1}{2} \...
- 31
2
votes
1
answer
80
views
Product of Majorana operators after a orthogonal transformation
The question I want to ask is the following:
There are $N$ Majorana fermion modes: $\gamma_1, \gamma_2, \dots, \gamma_N$, and they satisfy the anti-commutation relation:
$\{ \gamma_i, \gamma_j \} = 2\...
- 1,181
2
votes
0
answers
98
views
Must spin glasses really have an exponential density of states close to the ground state?
I'm a complete beginner to spin glasses. I'm not even sure of the definition; I've mostly seen examples, like Sherrington-Kirkpatric with all-all pairwise normally distributed Ising interactions. ...
- 2,292
2
votes
1
answer
178
views
Reduced density matrix of the edge spin-1/2 in AKLT spin chain
I am trying to understand the paper titled, "Entanglement in a Valence-Bond-Solid State" by Fan, Korepin, and Roychowdhury (https://arxiv.org/abs/quant-ph/0406067).
I was able to understand the ...
- 41
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
2
votes
0
answers
83
views
Spin Transition Energies
I am reading a paper:
http://arxiv.org/ftp/arxiv/papers/1305/1305.2445.pdf
On p. 22, the following Hamiltonian is given:
$$ H = \mu_B g \mathbf{B} \cdot \mathbf{S} + D(S_Z^2+\frac{1}{3}S(S+1)) + E(...
- 79
1
vote
0
answers
76
views
Non-degeneracy of the ground states of quantum spin models
It is known that the ground state of some quantum spin models is non-degenerate. For example, the ground states of the quantum Ising model and the ferromagnetic Heisenberg model on the subspace of a ...
- 5,697
1
vote
0
answers
53
views
Ising configuration after rotation in one sub-lattice
I do not understand Eq. (5.9) in Auerbach's book Interacting electrons an quantum magnetism. Consider the general spin-$S$ Heisenberg model on a bipartite lattice with $N$ sites:
$$
H = \frac{1}{2} \...
- 660
1
vote
0
answers
50
views
What is meant by spin temperature in the context of ultrafast demagnetization's three-temperature model?
Ultrafast demagnetization and associated fields often refer to the three-temperature model introduced by Beaurepaire. As the abstract says:
The relaxation processes of electrons and spins systems ...
- 46
1
vote
0
answers
109
views
Bogoliubov-Valatin transformation generalisation
Considering the following Heisenberg Hamiltonian (with spin $S$ , and $J<0$ for the case of an antiferromagnet) when we only consider interactions between first neighbors in a square lattice in the ...
- 1,124
1
vote
1
answer
110
views
Writing down a Hamiltonian that couples spin and phonons
I am studying spin dynamics and am trying to write down a Hamiltonian that couples the spins with the phonons. I have the following interacting spin Hamiltonian
$$H_{s}=\sum h_{i}S_{i}+H_{\text{...
- 21