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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2511.20762 |
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| _version_ | 1866908676467458048 |
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| author | Tiwana, Karan Tilloy, Antoine |
| author_facet | Tiwana, Karan Tilloy, Antoine |
| contents | Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for models with multiple fields, unless a regularity condition is satisfied. This has so far restricted the use of RCMPS to toy models with a single self-interacting field. We address this long standing problem by introducing a Riemannian optimization framework, that allows to minimize the energy density over the regular submanifold of multi-field RCMPS, and thus to retain purely variational results. We demonstrate its power on a model of two interacting scalar fields in $1+1$ dimensions. The method captures distinct symmetry-breaking phases, and the signature of a Berezinskii-Kosterlitz-Thouless (BKT) transition along an $O(2)$-symmetric parameter line. This makes RCMPS usable for a far larger class of problems than before. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_20762 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Multi-Field Relativistic Continuous Matrix Product States Tiwana, Karan Tilloy, Antoine Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory Relativistic continuous matrix product states (RCMPS) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their non-relativistic counterpart that makes them divergent for models with multiple fields, unless a regularity condition is satisfied. This has so far restricted the use of RCMPS to toy models with a single self-interacting field. We address this long standing problem by introducing a Riemannian optimization framework, that allows to minimize the energy density over the regular submanifold of multi-field RCMPS, and thus to retain purely variational results. We demonstrate its power on a model of two interacting scalar fields in $1+1$ dimensions. The method captures distinct symmetry-breaking phases, and the signature of a Berezinskii-Kosterlitz-Thouless (BKT) transition along an $O(2)$-symmetric parameter line. This makes RCMPS usable for a far larger class of problems than before. |
| title | Multi-Field Relativistic Continuous Matrix Product States |
| topic | Quantum Physics Strongly Correlated Electrons High Energy Physics - Theory |
| url | https://arxiv.org/abs/2511.20762 |