Relativistic continuous matrix product states (RCMPSs) are a powerful variational ansatz for quantum field theories of a single field. However, they inherit a property of their nonrelativistic counterpart that makes them divergent for models with multiple fields, unless a regularity condition is satisfied. This has so far restricted the use of RCMPSs to toy models with a single self-interacting field. We address this long-standing problem by introducing a Riemannian optimization framework, that allows us to minimize the energy density over the regular submanifold of multifield RCMPSs, 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 transition along an $O(2)$-symmetric parameter line. This makes RCMPSs usable for a far larger class of problems than before.

Close

PrevNext

View figure in article

• Matrix product states
• Optimization problems
• Quantum field theory
• Tensor network methods
• Variational approach