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

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 ${\varphi }^4$ 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.

JHEP version, typos fixed in Appendix and eq. (23)

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• Truncated Conformal Space Approach for 2D Landau-Ginzburg Theories
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Cited by in corpus (13)

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• Exploring Hamiltonian Truncation in $\mathbf{d}=2+1$
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks
• Hamiltonian Truncation Effective Theory
• Enhancing Quantum Field Theory Simulations on NISQ Devices with Hamiltonian Truncation
• Hamiltonian Truncation Crafted for UV-divergent QFTs
• Variational method in relativistic quantum field theory without cutoff
• Tadpoles and vacuum bubbles in light-front quantization
• On computing non-equilibrium dynamics following a quench
• Higher-order structure of Hamiltonian truncation effective theory