All Questions
Tagged with spin-models quantum-spin
86
questions
2
votes
2
answers
108
views
Expressing the spin-1/2 operators in terms of the quantum rotor variables
In this paper, a spin-1/2 Hamiltonian is introduced on a cubic lattice [Eq. (12)]:
$$
H_c = -J \sum_{\Box} (S_1^+ S_2^-S_3^+S_4^- + \text{H.c.}),
$$
where the sum runs over all plaquettes of the cubic ...
- 49
3
votes
0
answers
44
views
What $(2+0)d$ classical model becomes the $(1+1)d$ Heisenberg model?
The $(1+1)d$ transverse-field Ising chain is closely related to the $(2+0)d$ Ising model. In particular, the $(2+0)d$ classical Ising model has a transfer matrix that can be written suggestively as $e^...
- 2,292
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:
$$H = -\frac{1}{2}|J| \sum_{i,\vec{\delta}} \left[\frac{1}{2}(S_i^+S^-_{i+\vec{\delta}} + S_i^-S^+_{i+\vec{\delta}})...
- 70.2k
7
votes
1
answer
209
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Why is $H = J \sum_i (S^x_i S^x_{i+1} + S^y_iS^y_{i+1})$ always gapless for any spin $S$?
In the following I have in mind antiferromagnetic spin chains in periodic boundary conditions on a chain of even length $L$.
Consider the spin-$S$ spin chain
$$H = J \sum_{i=1}^L (S^x_i S^x_{i+1} + S^...
- 978
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
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
53
views
Diagonalizing the all-to-all quantum spin model (quantum Curie-Weiss) with uniform couplings
I am interested in diagonalizing the all-to-all quantum spin model
\begin{align}
\hat{H} = \frac{1}{2}\sum_{i,j \neq i} \hat{S}_i \cdot \hat{S}_j
\end{align}
or, if possible, a more general form ...
- 13.1k
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 ...
- 5,697
2
votes
1
answer
80
views
Product of Majorana operators after a orthogonal transformation
The question I want to ask is the following:
There are $N$ Majorana fermion modes: $\gamma_1, \gamma_2, \dots, \gamma_N$, and they satisfy the anti-commutation relation:
$\{ \gamma_i, \gamma_j \} = 2\...
- 978
2
votes
1
answer
2k
views
Integrability of quantum spin models
Based on this wiki page: https://en.wikipedia.org/wiki/Heisenberg_model_(quantum)
The XXZ model is exactly Bethe ansatz solvable, but based on this paper (pape 5): https://arxiv.org/abs/1011.0380, the ...
- 620
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
60
views
Breaking a classical ground state degeneracy by a quantum term and order-by-disorder
Let’s assume we have a Hamiltonian for spin-1/2 particles with two terms, a classical interaction term and a “quantum” (non-diagonal) term. For simplicity, let’s assume that the quantum term is a ...
- 28.4k
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
3
votes
1
answer
336
views
Conserved charge in Density Matrix Renormalization Group (DMRG)
Currently I am facing a problem which relates to the conserved quantities in DMRG. I use old-fashioned DMRG (Steven White approach) to compute the ground state of certain models. However, the ground ...
- 207k
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