Expectation values of local operators in phi^4 theory with a magnetic line defect are computed non-perturbatively using relativistic continuous matrix product states, by rotating Euclidean time so the defect becomes an extended operator in the bulk vacuum.
Variational method in relativistic quantum field theory without cutoff
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abstract
The variational method is a powerful approach to solve many-body quantum problems non perturbatively. However, in the context of relativistic quantum field theory (QFT), it needs to meet 3 seemingly incompatible requirements outlined by Feynman: extensivity, computability, and lack of UV sensitivity. In practice, variational methods break one of the 3, which translates into the need to have an IR or UV cutoff. In this letter, I introduce a relativistic modification of continuous matrix product states that satisfies the 3 requirements jointly in 1+1 dimensions. I apply it to the self-interacting scalar field, without UV cutoff and directly in the thermodynamic limit. Numerical evidence suggests the error decreases faster than any power law in the number of parameters, while the cost remains only polynomial.
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A relativistic continuous matrix product state study of field theories with defects
Expectation values of local operators in phi^4 theory with a magnetic line defect are computed non-perturbatively using relativistic continuous matrix product states, by rotating Euclidean time so the defect becomes an extended operator in the bulk vacuum.