Nonperturbative dynamics of (2+1)d ϕ 4-theory from Hamiltonian truncation
Nikhil Anand (Department of Physics, McGill University, 845 Sherbrooke St W, Montréal, QC, H3A 1B2, Canada); Emanuel Katz (Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA, 02215, USA); Zuhair Khandker (Department of Physics, Boston University, 590 Commonwealth Avenue, Boston, MA, 02215, USA); Matthew Walters (Theoretical Physics Department, CERN, Geneva 23, 1211, Switzerland, Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, CH-1015, Switzerland)
We use Lightcone Conformal Truncation (LCT)—a version of Hamiltonian truncation — to study the nonperturbative, real-time dynamics of ϕ 4-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 ϕ 4-theory in lightcone quantization. We then use LCT with this counterterm prescription to study ϕ 4-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.