All Questions
Tagged with spin-models spin-chains
66
questions
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
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
$$H = J \sum_{i=1}^L (S^x_i S^x_{i+1} + S^...
- 978
3
votes
1
answer
147
views
What is the signal of a spin wave?
From what I understand, for example in the Ising model, we can probe the correlation function via neutron scattering, and the correlation function gives the magnetic susceptibility for the system. Is ...
- 2,829
0
votes
1
answer
154
views
Troubles with Haldane Shastry Spin Chain
I'm reading the article "Exact solution of an S=1/2 Heisenberg antiferromagnetic chain with long-ranged interactions", which shows how to solve the problem of a long range-inverse squared ...
- 12.1k
2
votes
1
answer
134
views
Phase transitions in the XXZ model
Consider the one-dimensional quantum XXZ model defined by the Hamiltonian:
$$
H = J \sum_{i} \left (X_i X_{i+1} + Y_i Y_{i+1} + \Delta Z_i Z_{i+1} \right).
$$
First, let us focus at zero ...
- 368
0
votes
0
answers
52
views
Generating Matrix Product States from a (random) vector
I try to decomposite an arbitrary quantum state into a matrix product state. For this i follow this paper by U. Schollwöck where especially section 4.1.3 is relevant.
So far I did the following:
...
- 8,094
7
votes
1
answer
395
views
Kosterlitz-Thouless in the XXZ chain: instanton condensation?
The anisotropic spin-$\frac{1}{2}$ Heisenberg chain $$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 ...
- 1
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 ...
- 620
0
votes
0
answers
15
views
Tunneling lowers the energy of a ground state superposition of spins up and down in the quantum Ising model
Considering an Ising model in the quantum scenario in quantum spatial dimension d=1 (that corresponds to classical D=2=d+1 dimension). Starting with the Ising model hamiltonian under the approximation ...
- 310
2
votes
1
answer
676
views
Transverse-field Ising model in the presence of a longitudinal field - ferromagnetic phase diagram
I am wondering what is the phase diagram of the transverse-field Ising model in the presence of a longitudinal field, in particular, a one-dimensional spin-1/2 chain with ferromagnetic interactions. ...
- 29
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}\...
- 20.8k
-1
votes
1
answer
248
views
Calculate partition function of 1D quantum Heisenberg models?
For the 1D Quantum Heisenberg Spin Model:
$\displaystyle {\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}^z + h\...
- 20.8k
1
vote
0
answers
70
views
Emergent higher symmetry breaking without topological order?
In this paper prof. Wen states that (p.6)
a spontaneous higher symmetry broken state always corresponds to a topologically ordered state.
Are there examples of simple (or not) quantum spin models ...
- 29
1
vote
0
answers
77
views
Exact ground state degeneracy for quantum spin system with non commuting terms and its quantum phase transition?
Let's say I have a 2D quantum spin model of N spin-1/2 particles, with two terms:
$$
H = -J \sum_N \prod_{i \in G} \sigma^x_i - h \sum_N \prod_{i \in G'} \sigma^z_i
$$
The first is a collection of ...
- 29
0
votes
1
answer
102
views
Integrability of spin central model
I have a central model of this form $$H = \sum_{i=1}^{N} S^z_0\otimes S^z_i$$ where the $S^z_i$ acts on the $i$th element of the environment, i.e. the Hilbert space is of the following form $\mathcal{...
- 13.1k