Bootstrapping 2d ϕ 4 theory with Hamiltonian truncation data
Hongbin Chen (Department of Physics, Boston University, Boston, MA, 02215, U.S.A.); A. Fitzpatrick (Department of Physics, Boston University, Boston, MA, 02215, U.S.A.); Denis Karateev (Philippe Meyer Institute, Physics Department École Normale Supérieure (ENS), Université PSL, 24 rue Lhomond, Paris, F-75231, France)
We combine the methods of Hamiltonian Truncation and the recently proposed generalisation of the S-matrix bootstrap that includes local operators to determine the two-particle scattering amplitude and the two-particle form factor of the stress tensor at s > 0 in the 2d ϕ 4 theory. We use the form factor of the stress tensor at s ≤ 0 and its spectral density computed using Lightcone Conformal Truncation (LCT), and inject them into the generalized S-matrix bootstrap set-up. The obtained results for the scattering amplitude and the form factor are fully reliable only in the elastic regime. We independently construct the “pure” S-matrix bootstrap bounds (bootstrap without including matrix elements of local operators), and find that the sinh-Gordon model and its analytic continuation the “staircase model” saturate these bounds. Surprisingly, the ϕ 4 two-particle scattering amplitude also very nearly saturates these bounds, and moreover is extremely close to that of the sinh-Gordon/staircase model.