All Questions
Tagged with spin-chains integrable-systems
20
questions
1
vote
0
answers
35
views
Gap of the XXZ model in fixed magnetisation sectors
I am wondering whether it is known, or whether it can easily seen from the Bethe ansatz solution, what the gap of the spin-1/2 XXZ model of finite size $N$ with periodic boundary conditions
($H=\sum\...
- 51
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
-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\...
- 99
0
votes
1
answer
102
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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{...
- 565
2
votes
0
answers
61
views
Connection between diffusion and non-integrable 1D spin chains
My question concerns non-integrable (à la Bethe) 1D spin chains.
Consider, for example, the 1D non-integrable Ising model
\begin{equation}
H = \sum_{i \in \mathbb{Z}}\sigma_{i}^{z} \sigma_{i+1}^{z} + ...
- 53
2
votes
1
answer
87
views
What is the $XXX_s$ Hamiltonian in terms of $\vec{S}_i \cdot \vec{S}_{i+1}$?
Faddeev, Takhtajan, and others united and discovered many integrable models through the Algebraic Bethe Ansatz. For example, the integrable spin-1/2 Heisenberg model
$$H_{1/2} = \sum_{i=1}^L \vec{S}_i ...
- 2,292
1
vote
0
answers
204
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Parity of XYZ model ground state
I am considering the XYZ Hamiltonian (with PBC) $$\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{...
1
vote
0
answers
104
views
Unphysical Solution of the Bethe Ansatz
I actually want to ask an elementary question regarding the algebraic Bethe-Ansatz.
Say I have constructed the Bethe Ansatz Equations (BAE) in the algebraic framework with pseudovacuum $\phi$, $B(u)$ ...
- 309
3
votes
1
answer
446
views
XXZ chain exact ground state energy
I would like to know the analytical expression of the ground state energy of the XXZ model, if such formula exists (probably from a Bethe Ansatz solution) and if it is valid in all parameter regimes.
- 325
0
votes
1
answer
154
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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 ...
- 162
1
vote
1
answer
132
views
Algebraic Bethe Ansatz state generator problem
Given $B(\lambda)=T^0_1 (\lambda)$ the component of the monodromy matrix T that creates a state, $\lambda$ the spectral parameter and $| \Omega \rangle$ the reference ground state,
In "Quantum Groups ...
- 639
2
votes
1
answer
245
views
Integrability of generalized Richardson-Hubbard model
Recently I got a bit interested in the possibility of finding spectrum of few interesting class of lattice quantum mechanical hamiltonians like Richardson's pairing hamiltonian, 1D Hubbard hamiltonian,...
- 1,108
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
0
votes
0
answers
89
views
Elliptic R-matrix and Yang Baxter solution for XYZ model [duplicate]
in the framework of QISM, How can i derive the R-matrix for XYZ Heisenberg model?
- 162
1
vote
0
answers
104
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$R$ matrix for XYZ spin chain [duplicate]
Trying to understand how the Algebraic Bethe Ansatz works, I'm actually reading some papers and trying to apply for XXZ or XYZ model. But my problem is that I don't know how to find the R-matrix ...
- 162