RG flow from ϕ[superscript 4] theory to the 2D Ising model

Abstract

We study 1+1 dimensional ϕ[superscript 4] theory using the recently proposed method of conformal truncation. Starting in the UV CFT of free field theory, we construct a complete basis of states with definite conformal Casimir, C. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with C ≤ C[subscript max], we numerically diagonalize the Hamiltonian at strong coupling and study the resulting IR dynamics. We compute non-perturbative spectral densities of several local operators, which are equivalent to real-time, infinite-volume correlation functions. These spectral densities, which include the Zamolodchikov C-function along the full RG flow, are calculable at any value of the coupling. Near criticality, our numerical results reproduce correlation functions in the 2D Ising model. Keywords: Conformal Field Theory, Field Theories in Lower Dimensions, Nonperturbative Effects, Renormalization Group