RG flow from ϕ4 theory to the 2D Ising model

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

Research output: Contribution to journalArticlepeer-review


We study 1+1 dimensional ϕ4 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 CCmax, 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.
Original languageEnglish
Article number56
JournalJournal of High Energy Physics
Publication statusPublished - 16 Aug 2017


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


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