SciPost Commentary Page
Original publication:
| Title: | The Folded Spin-1/2 XXZ Model: I. Diagonalisation, Jamming, and Ground State Properties |
| Author(s): | Lenart Zadnik, Maurizio Fagotti |
| As Contributors: | Maurizio Fagotti · Lenart Zadnik |
| Journal ref.: | SciPost Physics Core 4, 010 |
| DOI: | https://doi.org/10.21468/SciPostPhysCore.4.2.010 |
| Date: | 2021-04-29 |
Abstract:
We study an effective Hamiltonian generating time evolution of states on intermediate time scales in the strong-coupling limit of the spin-1/2 XXZ model. To leading order, it describes an integrable model with local interactions. We solve it completely by means of a coordinate Bethe Ansatz that manifestly breaks the translational symmetry. We demonstrate the existence of exponentially many jammed states and estimate their stability under the leading correction to the effective Hamiltonian. Some ground state properties of the model are discussed.
Lenart Zadnik on 2021-12-21 [id 2041]
The explicit form of the duality transformation reported in the footnote 4 on page 10 is incomplete. In particular, the transformation of $\boldsymbol{\sigma}^y_L$ is missing. The correct expression for the transformation is provided below:
\begin{equation}
\notag
\boldsymbol \sigma_\ell^x\mapsto \begin{cases}
-\boldsymbol\sigma_1^y \prod_{j=2}^{L-1}\boldsymbol\sigma_j^z \boldsymbol\sigma_L^y,&\ell=1,\\
\boldsymbol\sigma_{\ell-1}^x\boldsymbol\sigma_\ell^x,&\ell>1,
\end{cases}
\qquad
\boldsymbol\sigma_\ell^y\mapsto \begin{cases}
\boldsymbol\sigma_1^x,&\ell=1,\\
\boldsymbol\sigma_{\ell-1}^x\boldsymbol\sigma_{\ell}^y\prod_{j=\ell+1}^{L-1}\boldsymbol\sigma_j^z\,\boldsymbol\sigma_L^y,&1<\ell<L,\\
-\boldsymbol\sigma_{L-1}^x\boldsymbol\sigma_L^z,&\ell=L,
\end{cases}
\qquad
\boldsymbol\sigma_\ell^z\mapsto \prod_{j=\ell}^{L-1}\boldsymbol\sigma_j^z\boldsymbol\sigma_L^y.
\end{equation}
We should stress that the explicit form of the duality transformation has not been used anywhere in the text, so this correction has no effect on the validity of any reported result.