All Questions
24
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:
$$H = -\frac{1}{2}|J| \sum_{i,\vec{\delta}} \left[\frac{1}{2}(S_i^+S^-_{i+\vec{\delta}} + S_i^-S^+_{i+\vec{\delta}})...
- 665
0
votes
0
answers
47
views
Spin-squeezing scaling with the number of particles in one-axis twisting hamiltonian
I am exploring the one axis twisting (OAT) hamiltonian $\hat{H}=\chi S_z^2$ with $S_z=\sum_{i=1}^N\frac{\sigma_z^i}{2}$ and considering the initial state to be $\left|\psi(0) \right>=\left|+x\right&...
- 219
0
votes
1
answer
4k
views
Ground state of the Heisenberg XXX model with a coupling?
I have a one-dimensional Heisenberg chain with a Magnetic field with $N$ sites with $J>0$
\begin{equation}
\mathcal{H} = -J \sum_{i = 1}^{N-1} \vec{S_i}\cdot \vec{S_{i+1}}- \sum_{i = 1}^N \vec{H}\...
- 904
0
votes
0
answers
30
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Do particles with higher spins have shorter wavelengths?
When they say that a half-spin particle 'spins' through 720° before returning to its original state, does that mean it has travelled twice as far as an otherwise identical particle possessing the same ...
- 4,509
0
votes
1
answer
112
views
Plaquette operator in Kitaev honeycomb model
In his honeycomb model, Kitaev defines link operators
\begin{equation}
K_{jk} = \begin{cases} \sigma_j^x \sigma_k^x & \text{if }(j, k)\text{ is an }x\text{-link;}\newline
\sigma_j^x \sigma_k^y &...
- 2,157
1
vote
0
answers
53
views
Ising configuration after rotation in one sub-lattice
I do not understand Eq. (5.9) in Auerbach's book Interacting electrons an quantum magnetism. Consider the general spin-$S$ Heisenberg model on a bipartite lattice with $N$ sites:
$$
H = \frac{1}{2} \...
- 660
3
votes
1
answer
237
views
Neel ordering on the square lattice vs mean-field AFM Heisenberg model
Question:
It seems like the Neel order of the AFM Heisenberg model on the square lattice is actually stronger than the (bipartite) fully-connected case. This seems counterintuitive. Am I simply wrong ...
- 321
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
0
votes
0
answers
52
views
Possible (Minor) Error in Original Lieb-Robinson Bound Paper
Introduction
I was reading through Lieb and Robinson's original paper introducing their eponymous bounds, and I came upon the following statement:
The task remains of corroborating our assertions ...
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
2
votes
2
answers
604
views
If a spin $\frac{1}{2}$ particle flips its sign after a 360° rotation, why don't theorists just say it rotated by 180°?
Usually, when a wave or wave-like object or system goes through a $180^{\circ}$ twist or turn or whatever, we say it is opposite to how it was oriented before, and if it came across its former self ...
- 4,509
0
votes
0
answers
121
views
Is it possible to construct an operator for $z$-component of spin for a 2D system?
Let's say we have an arrangement of spins in 2D space (as given in the below picture).
Assume that the $z$-axis is out of the plane and a spin (circled in red) makes an angle $\theta$ with the $x$-...
- 1,335
1
vote
0
answers
487
views
Commutator of Hamiltonian and the spin sum
For a 1-D Heisenberg quantum spin chain the Hamiltonian is given by:
$$H=-\sum_{j=0}^{N-1} J_{i,i+1}\boldsymbol{\sigma}_j^i \cdot\boldsymbol{\sigma}_{j+1}^i -\sum_{j=0}^{N}h_j\sigma_j^z$$
where $\...
- 11
2
votes
1
answer
307
views
Describing a subspace of a Hilbert space of $N$ spins 1/2
Consider having $N$ spins $1/2$, so the overall state of $N$ particles can be described by the total spin value $S=0 \ldots N/2$ (let us set $N$ to be even for simplicity), and the projection of the ...
- 133
2
votes
1
answer
53
views
Why is $\sum_{i=0}^N S_i^z S_{i+1}^z |\uparrow ... \downarrow_n ... \uparrow \rangle = \frac{1}{4}(N-4)$?
I am following these (http://edu.itp.phys.ethz.ch/fs13/int/SpinChains.pdf) lecture notes and I can't understand why given the following XXX Heisenberg hamiltonian
$$
\mathcal{H}=\frac{J N}{4}-J \sum_{...
- 1,544