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Higher-order structure of Hamiltonian truncation effective theory

Andrea Maestri*, Simone Rodini†, and Barbara Pasquini‡

  • *Contact author: andrea.maestri01@universitadipavia.it
  • †Contact author: simone.rodini@unipv.it
  • ‡Contact author: barbara.pasquini@unipv.it
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Phys. Rev. D 114, 016008 – Published 8 July, 2026

DOI: https://doi.org/10.1103/1wdr-ypw7

Abstract

We study the Hamiltonian truncation for the two-dimensional λϕ4 theory within the framework of Hamiltonian truncation effective theory, where truncation artifacts are mitigated through a systematic inclusion of corrective terms organized in inverse powers of the ultraviolet energy cutoff Emax. Building on the leading-order matching program, we develop two complementary extensions. First, we derive compact all-order expressions for the local matching corrections to the mass and quartic coupling by resumming infinite classes of diagrams sharing fixed topologies within the local approximation. Second, we extend the nonlocal sector by computing the next-to-next-to-local corrections contributing at O(Emax−4), following a continuum-first matching procedure, in which the effective corrections are computed in infinite volume and the spatial direction is subsequently recompactified to obtain a discrete basis of free-Hamiltonian eigenstates on which the truncated operator construction is implemented. Our results show that an increasingly rich operator basis is necessary to describe the theory beyond leading order.

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References (38)

  1. K. G. Wilson, Renormalization group and critical phenomena. 2. Phase space cell analysis of critical behavior, Phys. Rev. B 4, 3184 (1971).
  2. K. G. Wilson, Confinement of quarks, Phys. Rev. D 10, 2445 (1974).
  3. J. Berges, Introduction to nonequilibrium quantum field theory, AIP Conf. Proc. 739, 3 (2004).
  4. C. Wetterich, Exact evolution equation for the effective potential, Phys. Lett. B 301, 90 (1993).
  5. M. Creutz, Monte Carlo study of quantized SU(2) gauge theory, Phys. Rev. D 21, 2308 (1980).
  6. P. de Forcrand, Simulating QCD at finite density, Proc. Sci. LAT2009 (2009) 010 [arXiv:1005.0539].
  7. C. Gattringer and K. Langfeld, Approaches to the sign problem in lattice field theory, Int. J. Mod. Phys. A 31, 1643007 (2016).
  8. J. B. Kogut and L. Susskind, Hamiltonian formulation of Wilson’s lattice gauge theories, Phys. Rev. D 11, 395 (1975).
  9. M. C. Bañuls and K. Cichy, Review on novel methods for lattice gauge theories, Rep. Prog. Phys. 83, 024401 (2020).
  10. P. Silvi, E. Rico, T. Calarco, and S. Montangero, Lattice gauge tensor networks, New J. Phys. 16, 103015 (2014).
  11. D. B. Kaplan and J. R. Stryker, Gauss’s law, duality, and the Hamiltonian formulation of U(1) lattice gauge theory, Phys. Rev. D 102, 094515 (2020).
  12. R. C. Brower, D. Berenstein, and H. Kawai, Lattice gauge theory for a quantum computer, Proc. Sci. LATTICE2019 (2020) 112 [arXiv:2002.10028].
  13. V. P. Yurov and A. B. Zamolodchikov, Truncated conformal space approach to scaling Lee-Yang model, Int. J. Mod. Phys. A 05, 3221 (1990).
  14. V. P. Yurov and A. B. Zamolodchikov, Truncated fermionic space approach to the critical 2-D Ising model with magnetic field, Int. J. Mod. Phys. A 06, 4557 (1991).
  15. G. Feverati, F. Ravanini, and G. Takacs, Truncated conformal space at c=1, nonlinear integral equation and quantization rules for multi—soliton states, Phys. Lett. B 430, 264 (1998).
  16. T. Rakovszky, M. Mestyán, M. Collura, M. Kormos, and G. Takács, Hamiltonian truncation approach to quenches in the Ising field theory, Nucl. Phys. B911, 805 (2016).
  17. P. Schmoll, J. Naumann, A. Nietner, J. Eisert, and S. Sotiriadis, Hamiltonian truncation tensor networks for quantum field theories, arXiv:2312.12506.
  18. R. Houtz and J. Ingoldby, Hamiltonian truncation framework for gauge theories on the interval, arXiv:2509.17890.
  19. M. Hogervorst, S. Rychkov, and B. C. van Rees, Truncated conformal space approach in d dimensions: A cheap alternative to lattice field theory?, Phys. Rev. D 91, 025005 (2015).
  20. J. Elias-Miró and E. Hardy, Exploring Hamiltonian truncation in d=2+1, Phys. Rev. D 102, 065001 (2020).
  21. H. Chen, A. L. Fitzpatrick, E. Katz, and Y. Xin, Giving Hamiltonian truncation a boost, J. High Energy Phys. 03 (2025) 043.
  22. N. Anand, A. L. Fitzpatrick, E. Katz, Z. U. Khandker, M. T. Walters, and Y. Xin, Introduction to lightcone conformal truncation: QFT dynamics from CFT data, arXiv:2005.13544.
  23. A. L. Fitzpatrick and E. Katz, Snowmass white paper: Hamiltonian truncation, arXiv:2201.11696.
  24. P. Giokas and G. Watts, The renormalisation group for the truncated conformal space approach on the cylinder, arXiv:1106.2448.
  25. S. Rychkov and L. G. Vitale, Hamiltonian truncation study of the ϕ4 theory in two dimensions, Phys. Rev. D 91, 085011 (2015).
  26. S. Rychkov and L. G. Vitale, Hamiltonian truncation study of the ϕ4 theory in two dimensions. II. The Z2 -broken phase and the Chang duality, Phys. Rev. D 93, 065014 (2016).
  27. J. Elias-Miro, M. Montull, and M. Riembau, The renormalized Hamiltonian truncation method in the large ET expansion, J. High Energy Phys. 04 (2016) 144.
  28. J. Elias-Miro, S. Rychkov, and L. G. Vitale, NLO renormalization in the Hamiltonian truncation, Phys. Rev. D 96, 065024 (2017).
  29. J. Elias-Miro, S. Rychkov, and L. G. Vitale, High-precision calculations in strongly coupled quantum field theory with next-to-leading-order renormalized Hamiltonian truncation, J. High Energy Phys. 10 (2017) 213.
  30. J. Ingoldby, M. Spannowsky, T. Sypchenko, S. Williams, and M. Wingate, Real-time scattering on quantum computers via Hamiltonian truncation, arXiv:2505.03878.
  31. P. Draper, L. Hidalgo, and A. Ilderton, Hamiltonian truncation and quantum simulation of strong-field QED beyond tree level, Phys. Rev. D 113, 056010 (2026).
  32. T. Cohen, K. Farnsworth, R. Houtz, and M. A. Luty, Hamiltonian truncation effective theory, SciPost Phys. 13, 011 (2022).
  33. E. Demiray, K. Farnsworth, and R. Houtz, Systematic improvement of Hamiltonian truncation effective theory, arXiv:2507.15941.
  34. O. Delouche, J. Elias Miro, and J. Ingoldby, Hamiltonian truncation crafted for UV-divergent QFTs, SciPost Phys. 16, 105 (2024).
  35. J. Elias Miro and J. Ingoldby, Effective Hamiltonians and counterterms for Hamiltonian truncation, J. High Energy Phys. 07 (2023) 052.
  36. J. Zinn-Justin, From Random Walks to Random Matrices, Oxford Graduate Texts (Oxford University Press, New York, 2019).
  37. https://github.com/AndreaMaestri01/HTET_Resum_NNLOC (2026).
  38. M. Diehl, R. Nagar, and F. J. Tackmann, ChiliPDF: Chebyshev interpolation for parton distributions, Eur. Phys. J. C 82, 257 (2022).

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Phys. Rev. D 114, 016008– Published 8 July, 2026
  • Received 24 February 2026
  • Accepted 23 April 2026
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