Matrix product states as thin torus limits of conformal correlators
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arXiv
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| Format: | Preprint |
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2025
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| author | Franco-Rubio, Adrián Cirac, J. Ignacio Sierra, Germán |
| author_facet | Franco-Rubio, Adrián Cirac, J. Ignacio Sierra, Germán |
| contents | We introduce one-parameter families of spin chain ansatz wavefunctions constructed from chiral conformal field theory correlators on a torus, with the modular parameter $τ$ serving as the deformation parameter. In the cylinder limit $τ\to\infty$, these wavefunctions reduce to infinite dimensional matrix product states. In contrast, in the thin torus limit $τ\to0$, they become finite bond dimension matrix product states (MPS). Focusing on families derived from the SU(2)$_1$ and SU(2)$_2$ Wess-Zumino-Witten models, we show that in the thin torus limit they reproduce known MPS ground states, such as those of the Majumdar-Ghosh and AKLT spin chains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_22735 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Matrix product states as thin torus limits of conformal correlators Franco-Rubio, Adrián Cirac, J. Ignacio Sierra, Germán Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory We introduce one-parameter families of spin chain ansatz wavefunctions constructed from chiral conformal field theory correlators on a torus, with the modular parameter $τ$ serving as the deformation parameter. In the cylinder limit $τ\to\infty$, these wavefunctions reduce to infinite dimensional matrix product states. In contrast, in the thin torus limit $τ\to0$, they become finite bond dimension matrix product states (MPS). Focusing on families derived from the SU(2)$_1$ and SU(2)$_2$ Wess-Zumino-Witten models, we show that in the thin torus limit they reproduce known MPS ground states, such as those of the Majumdar-Ghosh and AKLT spin chains. |
| title | Matrix product states as thin torus limits of conformal correlators |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2507.22735 |