Effective Hamiltonians and Counterterms for Hamiltonian Truncation

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.

arXiv comment43 pages, 3 figures, explanations improved and typos corrected

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• Testing the RG-flow $M(3,10)+{\varphi }_{1,7}\to M(3,8)$ with Hamiltonian Truncation
• Renormalized dual basis for scalable simulations of 2+1D compact quantum electrodynamics
• Higher-order structure of Hamiltonian truncation effective theory