Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions

TL;DR

This paper validates a Hamiltonian truncation method for strongly coupled quantum field theories, demonstrating its effectiveness in studying the two-dimensional Phi^4 theory and identifying the quantum phase transition.

Contribution

It introduces an improved analytic renormalization approach within the Hamiltonian truncation framework for better accuracy in strongly coupled theories.

Findings

Accurate spectrum calculations for 2D Phi^4 theory

Identification of the critical coupling for phase transition

Agreement with previous literature results

Abstract

We defend the Fock-space Hamiltonian truncation method, which allows to calculate numerically the spectrum of strongly coupled quantum field theories, by putting them in a finite volume and imposing a UV cutoff. The accuracy of the method is improved via an analytic renormalization procedure inspired by the usual effective field theory. As an application, we study the two-dimensional Phi^4 theory for a wide range of couplings. The theory exhibits a quantum phase transition between the symmetry-preserving and symmetry-breaking phases. We extract quantitative predictions for the spectrum and the critical coupling and make contact with previous results from the literature. Future directions to further improve the accuracy of the method and enlarge its scope of applications are outlined.