# High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation

## TL;DR

This paper introduces a refined Hamiltonian Truncation method for strongly coupled 2D quantum field theories, reducing UV cutoff dependence and improving spectral accuracy through cubic order renormalization, with potential applications in higher dimensions.

## Contribution

A novel Hamiltonian Truncation variant that integrates out high energy states at cubic order, enhancing accuracy and applicability in strongly coupled QFTs.

## Key findings

- Smaller UV cutoff dependence in spectra
- More accurate spectral results in 2D scalar theory
- Potential extension to higher-dimensional QFTs

## Abstract

Hamiltonian Truncation (a.k.a. Truncated Spectrum Approach) is an efficient numerical technique to solve strongly coupled QFTs in d=2 spacetime dimensions. Further theoretical developments are needed to increase its accuracy and the range of applicability. With this goal in mind, here we present a new variant of Hamiltonian Truncation which exhibits smaller dependence on the UV cutoff than other existing implementations, and yields more accurate spectra. The key idea for achieving this consists in integrating out exactly a certain class of high energy states, which corresponds to performing renormalization at the cubic order in the interaction strength. We test the new method on the strongly coupled two-dimensional quartic scalar theory. Our work will also be useful for the future goal of extending Hamiltonian Truncation to higher dimensions d >= 3.