Hamiltonian renormalisation VIII. P(Phi,2) quantum field theory

TL;DR

This paper applies Hamiltonian renormalisation to the self-interacting scalar field in two dimensions, successfully identifying the P(Phi,2) theory as a fixed point in the renormalisation flow.

Contribution

It extends Hamiltonian renormalisation methods to an interacting quantum field theory, specifically the P(Phi,2) model in two dimensions, demonstrating its non-perturbative construction.

Findings

The renormalisation flow converges to the P(Phi,2) fixed point.

The method confirms the non-perturbative constructibility of the theory.

The approach is limited to finite volume cases.

Abstract

In previous works in this series we focussed on Hamiltonian renormalisation of free field theories in all spacetime dimensions. In this paper we address the Hamiltonian renormalisation of the self-interacting scalar field in two spacetime dimensions with polynomial potential, called P(Phi,2). We consider only the finite volume case. The P(Phi,2) theory is one of the few interacting QFT's that can be rigorously constructed non-perturbatively. We find that our Hamiltonian renormalisation flow finds this theory indeed as a fixed point.