Dressed energy of the XXZ chain in the complex plane
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| _version_ | 1866909222550110208 |
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| author | Faulmann, Saskia Göhmann, Frank Kozlowski, Karol K. |
| author_facet | Faulmann, Saskia Göhmann, Frank Kozlowski, Karol K. |
| contents | We consider the dressed energy $\varepsilon$ of the XXZ chain in the massless antiferromagnetic parameter regime at $0 < Δ< 1$ and at finite magnetic field. This function is defined as a solution of a Fredholm integral equation of the second kind. Conceived as a real function over the real numbers it describes the energy of particle-hole excitations over the ground state at fixed magnetic field. The extension of the dressed energy to the complex plane determines the solutions to the Bethe Ansatz equations for the eigenvalue problem of the quantum transfer matrix of the model in the low-temperature limit. At low temperatures the Bethe roots that parametrize the dominant eigenvalue of the quantum transfer matrix come close to the curve ${\rm Re}\, \varepsilon (λ) = 0$. We describe this curve and give lower bounds to the function ${\rm Re}\, \varepsilon$ in regions of the complex plane, where it is positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2106_06732 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Dressed energy of the XXZ chain in the complex plane Faulmann, Saskia Göhmann, Frank Kozlowski, Karol K. Mathematical Physics Statistical Mechanics High Energy Physics - Theory We consider the dressed energy $\varepsilon$ of the XXZ chain in the massless antiferromagnetic parameter regime at $0 < Δ< 1$ and at finite magnetic field. This function is defined as a solution of a Fredholm integral equation of the second kind. Conceived as a real function over the real numbers it describes the energy of particle-hole excitations over the ground state at fixed magnetic field. The extension of the dressed energy to the complex plane determines the solutions to the Bethe Ansatz equations for the eigenvalue problem of the quantum transfer matrix of the model in the low-temperature limit. At low temperatures the Bethe roots that parametrize the dominant eigenvalue of the quantum transfer matrix come close to the curve ${\rm Re}\, \varepsilon (λ) = 0$. We describe this curve and give lower bounds to the function ${\rm Re}\, \varepsilon$ in regions of the complex plane, where it is positive. |
| title | Dressed energy of the XXZ chain in the complex plane |
| topic | Mathematical Physics Statistical Mechanics High Energy Physics - Theory |
| url | https://arxiv.org/abs/2106.06732 |