Nonperturbative dynamics of (2+1)d ϕ4-theory from Hamiltonian truncation

Nikhil Anand, Emanuel Katz, Zuhair U. Khandker, Matthew T. Walters

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We use Lightcone Conformal Truncation (LCT)—a version of Hamiltonian truncation — to study the nonperturbative, real-time dynamics of ϕ4-theory in 2+1 dimensions. This theory has UV divergences that need to be regulated. We review how, in a Hamiltonian framework with a total energy cutoff, renormalization is necessarily state-dependent, and UV sensitivity cannot be canceled with standard local operator counter-terms. To overcome this problem, we present a prescription for constructing the appropriate state-dependent counterterms for (2+1)d ϕ4-theory in lightcone quantization. We then use LCT with this counterterm prescription to study ϕ4-theory, focusing on the ℤ2 symmetry-preserving phase. Specifically, we compute the spectrum as a function of the coupling and demonstrate the closing of the mass gap at a (scheme-dependent) critical coupling. We also compute Lorentz-invariant two-point functions, both at generic strong coupling and near the critical point, where we demonstrate IR universality and the vanishing of the trace of the stress tensor.
Original languageEnglish
Article number190
JournalJournal of High Energy Physics
Publication statusPublished - 20 May 2021


  • hep-th
  • cond-mat.stat-mech
  • cond-mat.str-el
  • hep-lat


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