Boundary effects and the stability of the low energy spectrum of the AKLT model
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866912098713337856 |
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| author | Del Vecchio, Simone Fröhlich, Jürg Pizzo, Alessandro Ranallo, Alessio |
| author_facet | Del Vecchio, Simone Fröhlich, Jürg Pizzo, Alessandro Ranallo, Alessio |
| contents | In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the \emph{local, iterative Lie Schwinger block-diagonalization method} which allows us to control small interaction terms localized near the boundary of the chain that are responsible for the possible splitting of the ground-state energy of the AKLT Hamiltonian into energy levels separated by small gaps. This improves earlier results concerning the persistence of the so called \emph{bulk} gap in these models, besides illustrating the power of our general methods in a non-trivial application. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_02811 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Boundary effects and the stability of the low energy spectrum of the AKLT model Del Vecchio, Simone Fröhlich, Jürg Pizzo, Alessandro Ranallo, Alessio Mathematical Physics In this paper we study the low-lying spectrum of the AKLT model perturbed by small, finite-range potentials and with open boundary conditions imposed at the edges of the chain. Our analysis is based on the \emph{local, iterative Lie Schwinger block-diagonalization method} which allows us to control small interaction terms localized near the boundary of the chain that are responsible for the possible splitting of the ground-state energy of the AKLT Hamiltonian into energy levels separated by small gaps. This improves earlier results concerning the persistence of the so called \emph{bulk} gap in these models, besides illustrating the power of our general methods in a non-trivial application. |
| title | Boundary effects and the stability of the low energy spectrum of the AKLT model |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2308.02811 |