A relativistic continuous matrix product state study of field theories with defects

TL;DR

This paper introduces a novel RCMPS-based method to compute expectation values in 1+1D massive QFTs with line defects, enabling analysis across various regimes.

Contribution

It develops a new approach using Euclidean invariance and RCMPS to efficiently evaluate correlation functions in defect quantum field theories.

Findings

Successfully computed correlation functions in $$ theory with a magnetic line defect

Applicable across perturbative, strong coupling, critical, and symmetry-broken regimes

Demonstrates effectiveness of the RCMPS method for defect field theories

Abstract

We propose a method to compute expectation values in 1+1-dimensional massive Quantum Field Theories (QFTs) with line defects using Relativistic Continuous Matrix Product State (RCMPS). Exploiting Euclidean invariance, we use a quantization scheme where (imaginary) time runs perpendicularly to the defect. With this choice, correlation functions of local operators in the presence of the defect can be computed as expectation values of extended operators in the no-defect vacuum, which can be approximated by a homogeneous RCMPS. We demonstrate the effectiveness of this machinery by computing correlation functions of local bulk and defect operators in $\phi^4$ theory with a magnetic line defect, in perturbative, strong coupling, critical, and symmetry-broken regimes.