All Questions
Tagged with spin-models spin-chains
66
questions
7
votes
1
answer
867
views
Goldstone mode as spin wave in 2D?
I'm trying to understand how Goldstone modes destroy long range order in 1D and 2D spin lattice.
I started with a spin chain, using 1D XY-model, which has continuous symmetry. $H=- \sum_{<i j>} ...
- 314
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
$$H = J \sum_{i=1}^L (S^x_i S^x_{i+1} + S^...
- 2,292
7
votes
1
answer
395
views
Kosterlitz-Thouless in the XXZ chain: instanton condensation?
The anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$H = \sum_n S^x_n S^x_{n+1} + S^y_n S^y_{n+1} + \Delta S^z_n S^z_{n+1}$$ is known to have the same physics as the two-dimensional classical XY ...
- 9,081
6
votes
1
answer
259
views
Mathematical meaning for Algebraic Bethe Ansatz
I'm a mathematician who's trying to understand the meaning of Algebraic Bethe Ansatz. What I understood is that when dealing with quantum integrable models (like XXZ Heisenberg spin chain), one is ...
- 113
6
votes
1
answer
293
views
Zero modes $a_j\sim e^{-\kappa j}$ in a semi-infinite quantum Ising chain?
As a way of analyzing the performance of quantum annealing, I've been studying quantum diffusion in fermionizable lattice models with zero modes.
In particular, the 1+1D quantum Ising model, semi-...
- 985
5
votes
1
answer
1k
views
R-matrix for spin chains
In algebraic Bethe ansatz procedure, one of the central objects is the R-matrix satisfying the Yang-Baxter equation, but all the papers/books give directly its expression without deriving it, so my ...
- 162
5
votes
1
answer
1k
views
Some limiting cases of the Heisenberg XXZ model (2/2)
NOTE: Because this was a long question I have split it up in two different questions!
For a course on quantum integrability I am reading these notes.
(Franchini: Notes on Bethe Ansatz Techniques. ...
- 2,910
4
votes
1
answer
1k
views
Ground state magnetization of the Heisenberg XXZ chain
The Hamiltonian of the Heisenberg XXZ chain (without external field) has the form
$$
H = -J \sum_{n=1}^{N}\left(S_n^xS_{n+1}^x+ S_n^yS_{n+1}^y + \Delta S_n^zS_{n+1}^z\right).
$$
It is known that this ...
- 83
4
votes
2
answers
2k
views
Kagome Lattice: Spin-orbit coupling Hamiltonian in tight-binding models
Consider spin-orbit coupling (of strength $\lambda_1$) on lattice, with the below Hamiltonian
$$H = i \lambda_1 \sum_{<ij>} ~\frac{E_{ij} \times R_{ij}}{|E_{ij} \times R_{ij}|} \cdot \sigma ~...
- 359
4
votes
0
answers
47
views
Are strong correlations of boundary spins possible in the absence of long-range order in the bulk?
Question about one-dimensional models with short range interaction of quantum spins, such as transverse Ising and Heisenberg models. Are there any examples when, in the ground state of the system, the ...
- 5,697
4
votes
0
answers
230
views
Heisenberg equation of motion and continuum limit
Given the quite simple Hamiltonian
$$\hat{\mathcal{H}}=\sum_n\big(\hat{S}_n^+\hat{S}^-_{n+1}+\hat{S}_n^-\hat{S}^+_{n+1}\big)$$
on a 1D spin chain, it basically interchanges two spins lying next to ...
- 294
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
652
views
Jordan-Wigner transformation for lattice models without $U(1)$ symmetry
The Jordan-Wigner transformation is a powerful approach to studying one-dimensional spin models. The following dictionary between spin operators and creation/annihilation operators for fermions allows ...
- 759
3
votes
1
answer
1k
views
Heisenberg ferromagnet in continuum limit
I consider the case of the simple, say 2D, Heisenberg ferromagnet with exchange interaction between the nearest neighbors. The Hamiltonian is:
$$H = -J \sum_{<ij>} \mathbf S_i \mathbf S_j,$$
...
- 43