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We study 1+1 dimensional $\phi^4$ theory using the recently proposed methodof conformal truncation. Starting in the UV CFT of free field theory, weconstruct a complete basis of states with definite conformal Casimir,$\mathcal{C}$. We use these states to express the Hamiltonian of the fullinteracting theory in lightcone quantization. After truncating to states with$\mathcal{C} \leq \mathcal{C}_{\max}$, we numerically diagonalize theHamiltonian at strong coupling and study the resulting IR dynamics. We computenon-perturbative spectral densities of several local operators, which areequivalent to real-time, infinite-volume correlation functions. These spectraldensities, which include the Zamolodchikov $C$-function along the full RG flow,are calculable at any value of the coupling. Near criticality, our numericalresults reproduce correlation functions in the 2D Ising model.

RG Flow from $\phi^4$ Theory to the 2D Ising Model