Excitation Spectra of 1+1D Scalar Field Theories from Relativistic Continuous Matrix Product States

Abstract

In this thesis, we study the dynamics of 1+1D scalar field theories using the Relativistic Continuous Matrix Product States (RCMPS) framework. This framework is an extension of Matrix Product States (MPSs) to the continuum, yielding a variational class that is manifestly finite and requires no ultraviolet cutoff. We generalize the RCMPS formalism to compute the low-lying particle spectrum of the Sine-Gordon model, the φ⁴ theory, and the free theory with a mass perturbation. We calculate the mass of the lowest breather of the Sine-Gordon theory with excellent accuracy at a modest bond dimension D=16. Additionally, we compute the mass gap of the φ⁴ theory and find the critical coupling at which the Z₂ symmetry spontaneously breaks. Our results are in agreement with the literature, demonstrating the utility of RCMPSs as a variational tool for studying the dynamics of 1+1D strongly coupled scalar field theories.