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

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.

arXiv comment8 pages, 4 figures; v2: published version

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• NLO Renormalization in the Hamiltonian Truncation
• Tensor network analysis of critical coupling in two dimensional ${\varphi }^4$ theory
• $\lambda {\varphi }^4$ Theory I: The Symmetric Phase Beyond NNNNNNNNLO
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• Exploring Hamiltonian Truncation in $\mathbf{d}=2+1$
• Lightcone Effective Hamiltonians and RG Flows
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks
• New MC determination of the critical coupling in ${\varphi }_2^4$ theory
• Simple non-perturbative resummation schemes beyond mean-field: case study for scalar ${\varphi }^4$ theory in 1+1 dimensions
• Approaching the Self-Dual Point of the Sinh-Gordon model
• Introduction to Lightcone Conformal Truncation: QFT Dynamics from CFT Data
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• Hamiltonian Truncation Effective Theory
• Nonperturbative Matching Between Equal-Time and Lightcone Quantization
• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
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• Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models
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• Counterterms in Truncated Conformal Perturbation Theory
• Tadpoles and vacuum bubbles in light-front quantization
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• On computing non-equilibrium dynamics following a quench
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