Effective Hamiltonians and Counterterms for Hamiltonian Truncation

TL;DR

This paper develops a new method for applying Hamiltonian Truncation to UV-divergent Quantum Field Theories by deriving an Effective Hamiltonian that ensures spectral matching and consistency with conformal perturbation theory.

Contribution

It introduces a novel representation of the Effective Hamiltonian that handles UV divergences and non-local interactions in Hamiltonian Truncation for QFTs.

Findings

Effective Hamiltonian accurately matches spectra between UV and truncated theories.

The procedure is consistent with Conformal Perturbation Theory.

Non-local interactions in the Effective Hamiltonian can describe local QFTs.

Abstract

We outline a procedure for applying Hamiltonian Truncation to Quantum Field Theories (QFTs) that have UV divergences. To do this, we derive a novel representation of an Effective Hamiltonian which makes manifest some of its important properties (e.g. the non-perturbative matching of the spectra between the UV theory and the theory described by the Effective Hamiltonian). We check the consistency of our procedure using Conformal Perturbation Theory. Finally we comment on how the Effective Hamiltonian, which incorporates non-local interactions, describes a local QFT.