All Questions
Tagged with spin-chains hamiltonian
13
questions
0
votes
1
answer
72
views
Is there a name for a Heisenberg-like model, but instead of the ZZ operator, we have one that favor only spin-up-spin-up configurations?
I understand that the Quantum Heisenberg XXZ model in 1D has the form:
$$\hat H = \frac{1}{2} \sum_{j=1}^{N} (J_x \sigma_j^x \sigma_{j+1}^x + J_y \sigma_j^y \sigma_{j+1}^y + J_z \sigma_j^z \sigma_{j+1}...
- 700
0
votes
1
answer
53
views
How to handle Dzyaloshinkii-Moriya imaginary terms in Heisenberg chain?
The DM interaction has three coordinate-specific terms when splitting it up. Two of these, the DM-x and DM-z terms, are imaginary when we transform them into series of raising and lowering operators. ...
- 11
2
votes
1
answer
223
views
Jordan-Wigner Transformations on fermionic system
I've been trying to use Jordan-Wigner Transformations on a given fermionic Hamiltonian. The given Hamiltonian is: $$ \hat{H}= -\sum_{m=1}^{N}(J_z \hat{S}_{m}^{z} \hat{S}_{m+1}^{z} + \frac{J_{\perp}}{2}...
- 23
1
vote
0
answers
204
views
Parity of XYZ model ground state
I am considering the XYZ Hamiltonian (with PBC) $$\widehat{H}_{\mathrm{XYZ}}=\sum_{i=1}^{N} \left(\hat{\sigma}_{i}^{x} \hat{\sigma}_{i+1}^{x}+J_{y}\hat{\sigma}_{i}^{y} \hat{\sigma}_{i+1}^{y}+J_{z}\hat{...
0
votes
1
answer
241
views
The most general $SU(2)$ invariant spin-$1/2$ Hamiltonian on 5 sites
I have periodic chain of spins $s=1/2$. I want to know what is the most general $SU(2)$ invariant and translation-invariant Hamiltonian. My guess is:
$$\sum_i (j_1 S_i \cdot S_{i+1}+j_2 S_i \cdot S_{i+...
- 1
0
votes
1
answer
58
views
Balance the units of the following hamiltonian
The following image is taken from an article and shows the hamiltonian of a spin chain model. I knew that the dimensional units in an equation must balance. To ensure this, the author took a procedure ...
- 233
1
vote
1
answer
615
views
One-dimensional Ising Model in a three spin chain
I have a system of three aligned spins with $S=\frac{1}{2}$. There are interactions between nearest neighbors, and each spin has a magnetic moment. The Hamiltonian of the system is:
$$H=J[S_z(1)S_z(2) ...
- 11
0
votes
1
answer
298
views
Hamiltonian for a 1D spin chain [closed]
I am trying to implement the Lanczos algorithm to tridiagonalize the Hamiltonian for a 1D spin chain of length $L$, but I am unable to decipher from my professor's notes (here's a link), what the ...
- 416
1
vote
1
answer
2k
views
Hamiltonian Matrix for XXZ Model
Given the XXZ model Hamiltonian,
$H = -\frac{1}{2}\sum^{N}_{i}(\sigma_{i}^{x}\sigma_{i+1}^{x}+\sigma_{i}^{y}\sigma_{i+1}^{y}+\Delta\sigma_{i}^{z}\sigma_{i+1}^{z})$
The two-site Hamiltonian reads
$H ...
- 51
1
vote
2
answers
1k
views
Block diagonalizing a spin-chain Hamiltonian
$\newcommand{\ket}[1]{\left|#1\right>}$
I am learning about exact diagonalization methods, currently following this explanation. My question is in regards to the part where we utilize the fact ...
- 3,710
2
votes
0
answers
71
views
Change in ground state after perturbing a hamiltonian
Lets consider a spin $\frac{1}{2}$ chain with $n$ spins and an associated local hamiltonian $H= \sum_i h_{i,i+1}$. We also assume that $\|h_{i,i+1}\|_{\infty} \leq 1$. In this question, we will be ...
- 771
30
votes
1
answer
6k
views
Detailed derivation and explanation of the AKLT Hamiltonian
I am trying to read the original paper for the AKLT model,
Rigorous results on valence-bond ground states in antiferromagnets. I Affleck, T Kennedy, RH Lieb and H Tasaki. Phys. Rev. Lett. 59, 799 (...
- 629
4
votes
2
answers
779
views
Undefined amplitudes in the Coordinate Bethe Ansatz for the XXX model?
Rather specific question for someone familiar with the Coordinate Bethe Ansatz... I am considering the Heisenberg XXX-model, consisting of a one-dimensional chain of L sites with a spin-1/2 particle ...
- 1,232