Multi-Field Relativistic Continuous Matrix Product States

Karan Tiwana; Antoine Tilloy

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arXiv · 2511.20762

Multi-Field Relativistic Continuous Matrix Product States

Karan Tiwana·Antoine Tilloy

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Abstract

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.

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Karan Tiwana, Antoine Tilloy. 2025-11-25. Multi-Field Relativistic Continuous Matrix Product States. https://arxiv.org/abs/2511.20762

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