All Questions
Tagged with spin-models quantum-spin
86
questions
17
votes
2
answers
1k
views
What is the momentum canonically conjugate to spin in QM?
In Kopec and Usadel's Phys. Rev. Lett. 78.1988, a spin glass Hamiltonian is introduced in the form:
$$
H = \frac{\Delta}{2}\sum_i \Pi^2_i - \sum_{i<j}J_{ij}\sigma_i \sigma_j,
$$
where the ...
- 321
8
votes
2
answers
358
views
Is there a spin glass version of Prince Rupert's Drop?
Spin Glasses are known to converge to their ground state under Simulated Annealing.
The word choice is especially interesting since annealing is also the name of a process performed on actual glass. ...
- 4,841
7
votes
1
answer
209
views
Why is $H = J \sum_i (S^x_i S^x_{i+1} + S^y_iS^y_{i+1})$ always gapless for any spin $S$?
In the following I have in mind antiferromagnetic spin chains in periodic boundary conditions on a chain of even length $L$.
Consider the spin-$S$ spin chain
$$H = J \sum_{i=1}^L (S^x_i S^x_{i+1} + S^...
- 2,292
6
votes
3
answers
12k
views
Nuclear Spin of Sodium 23
I am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and ...
- 95
6
votes
1
answer
259
views
Mathematical meaning for Algebraic Bethe Ansatz
I'm a mathematician who's trying to understand the meaning of Algebraic Bethe Ansatz. What I understood is that when dealing with quantum integrable models (like XXZ Heisenberg spin chain), one is ...
- 113
5
votes
1
answer
1k
views
Some limiting cases of the Heisenberg XXZ model (2/2)
NOTE: Because this was a long question I have split it up in two different questions!
For a course on quantum integrability I am reading these notes.
(Franchini: Notes on Bethe Ansatz Techniques. ...
- 2,910
4
votes
1
answer
201
views
Clebsch-Gordan coefficients, spin networks and intertwiners
After spending some time with LQG books and articles i have still some problems regarding concepts of this theory.
Spin network is built from lines labeled by spin label $j$ and since angular momentum ...
4
votes
0
answers
141
views
Energy gap of a Heisenberg model on bipartite lattices
Consider the antiferromagnetic Heisenberg model on some "graph" where each vertex corresponds to a spin-1/2 and the edges represent interaction between the vertices, i.e.,
\begin{equation}
\...
- 321
4
votes
0
answers
89
views
Operator inequality between the Heisenberg Hamiltonian and the total spin
Consider a collection of $N$ spin-1/2 particles (qubits) with total spin
$$\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
1
answer
216
views
How do we determine the statistics and spin of quasi-particles?
I am considering the Heisenberg XXZ model at the moment. In the literature it says that (in the $J\Delta\rightarrow\infty$ limit, i.e. the ferromagnetic Ising regime) one can either view low-energy ...
- 2,910
3
votes
2
answers
241
views
Do spins add when particles combine symmetrically?
Suppose I have three spin $s$ particles. What are the possible spins of a symmetric combination of these three particles? Will one of the states always have spin $3s$?
Perhaps the above question is ...
- 85
3
votes
1
answer
202
views
Weyssenhoff fluid and Frenkel condition
A Weyssenhoff fluid is a continuos fluid with spin. The spin is described by an antisimmetric tensor $s{_{ab}}=s{_{[ab]}}$ satisfying the Frenkel condition
\begin{equation}
s{_{ab}}u{^b}=0
\end{...
- 565
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
3
votes
1
answer
559
views
Static spin structure factor VS equal-time spin structure factor
It looks like many papers (maybe all papers containing "static spin structure factor") use the terminology, static spin structure factor, to refer to the equal-time spin structure factor ...
- 123