Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2406.09889 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917862108561408 |
|---|---|
| author | Azhari, Mouhcine Klümper, Andreas |
| author_facet | Azhari, Mouhcine Klümper, Andreas |
| contents | In this paper, we investigate the spectral properties of the staggered six-vertex model with ${\cal Z}_2$ symmetry for arbitrary system sizes $L$ using non-linear integral equations (NLIEs). Our study is motivated by two key questions: what is the accuracy of results based on the ODE/IQFT correspondence in the asymptotic regime of large system sizes, and what is the optimal approach based on NLIE for analyzing the staggered six-vertex model?
We demonstrate that the quantization conditions for low-lying primary and descendant states, derived from the ODE/IQFT approach in the scaling limit, are impressively accurate even for relatively small system sizes. Specifically, in the anisotropy parameter range $π/4 < γ< π/2$, the difference between NLIE and ODE/IQFT results for energy and quasi-momentum eigenvalues is of order $\mathcal{O}(L^{-2})$.
Furthermore, we present a unifying framework for NLIEs, distinguishing between versions with singular and regular kernels. We provide a compact derivation of NLIE with a singular kernel, followed by an equivalent set with a regular kernel. We address the stability issues in numerical treatments and offer solutions to achieve high-accuracy results, validating our approach for system sizes ranging from $L=2$ to $L=10^{24}$.
Our findings not only validate the ODE/IQFT approach for finite system sizes but also enhance the understanding of NLIEs in the context of the staggered six-vertex model. We hope the insights gained from this study have significant implications for resolving the spectral problem of other lattice systems with emergent non-compact degrees of freedom and provide a foundation for future research in this domain. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09889 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Managing Singular Kernels and Logarithmic Corrections in the Staggered Six-Vertex Model Azhari, Mouhcine Klümper, Andreas Statistical Mechanics High Energy Physics - Theory In this paper, we investigate the spectral properties of the staggered six-vertex model with ${\cal Z}_2$ symmetry for arbitrary system sizes $L$ using non-linear integral equations (NLIEs). Our study is motivated by two key questions: what is the accuracy of results based on the ODE/IQFT correspondence in the asymptotic regime of large system sizes, and what is the optimal approach based on NLIE for analyzing the staggered six-vertex model? We demonstrate that the quantization conditions for low-lying primary and descendant states, derived from the ODE/IQFT approach in the scaling limit, are impressively accurate even for relatively small system sizes. Specifically, in the anisotropy parameter range $π/4 < γ< π/2$, the difference between NLIE and ODE/IQFT results for energy and quasi-momentum eigenvalues is of order $\mathcal{O}(L^{-2})$. Furthermore, we present a unifying framework for NLIEs, distinguishing between versions with singular and regular kernels. We provide a compact derivation of NLIE with a singular kernel, followed by an equivalent set with a regular kernel. We address the stability issues in numerical treatments and offer solutions to achieve high-accuracy results, validating our approach for system sizes ranging from $L=2$ to $L=10^{24}$. Our findings not only validate the ODE/IQFT approach for finite system sizes but also enhance the understanding of NLIEs in the context of the staggered six-vertex model. We hope the insights gained from this study have significant implications for resolving the spectral problem of other lattice systems with emergent non-compact degrees of freedom and provide a foundation for future research in this domain. |
| title | Managing Singular Kernels and Logarithmic Corrections in the Staggered Six-Vertex Model |
| topic | Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2406.09889 |