The renormalized Hamiltonian truncation method in the large $E_T$ expansion

TL;DR

This paper introduces a new, general method for calculating exact corrections in Hamiltonian truncation, demonstrated on 2D phi^4 theory, improving numerical efficiency and accuracy at strong coupling.

Contribution

The paper presents a novel approach to compute exact Hamiltonian truncation corrections at any order, with explicit calculations for 2D phi^4 theory and new approximations for faster numerical results.

Findings

Exact g^2 and some g^3 contributions computed for 2D phi^4 theory.

Coefficients are given by phase space integrals.

New approximations improve numerical speed and accuracy.

Abstract

Hamiltonian Truncation Methods are a useful numerical tool to study strongly coupled QFTs. In this work we present a new method to compute the exact corrections, at any order, in the Hamiltonian Truncation approach presented by Rychkov et al. in Refs. [1-3]. The method is general but as an example we calculate the exact $g^2$ and some of the $g^3$ contributions for the $\phi^4$ theory in two dimensions. The coefficients of the local expansion calculated in Ref. [1] are shown to be given by phase space integrals. In addition we find new approximations to speed up the numerical calculations and implement them to compute the lowest energy levels at strong coupling. A simple diagrammatic representation of the corrections and various tests are also introduced.