RG Flow from ${\varphi }^4$ Theory to the 2D Ising Model

Abstract

We study 1+1 dimensional ${\varphi }^4$ 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, $\mathcal{C}$. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with $\mathcal{C}\le {\mathcal{C}}_{\max }$, 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.

31+12 pages

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• A solution of 2D QCD at Finite $N$ using a conformal basis
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Cited by in corpus (26)

• Gapless topological phases and symmetry-enriched quantum criticality
• NLO Renormalization in the Hamiltonian Truncation
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• $\lambda {\varphi }^4$ Theory I: The Symmetric Phase Beyond NNNNNNNNLO
• The Lorentzian inversion formula and the spectrum of the 3d O(2) CFT
• Quantum simulation of quantum field theories as quantum chemistry
• $\lambda {\varphi }^4$ Theory II: The Broken Phase Beyond NNNN(NNNN)LO
• Lightcone Effective Hamiltonians and RG Flows
• Thermalization and chaos in a 1+1d QFT
• Hamiltonian Truncation Effective Theory
• Nonperturbative Matching Between Equal-Time and Lightcone Quantization
• Momentum space CFT correlators for Hamiltonian truncation
• Effective Hamiltonians and Counterterms for Hamiltonian Truncation
• RG Flows and Thermofield-Double States in Holography
• Self-Dualities and Renormalization Dependence of the Phase Diagram in 3d $O(N)$ Vector Models
• Form Factors and Spectral Densities from Lightcone Conformal Truncation
• Towards a nonperturbative construction of the $S$-matrix
• Transitioning from equal-time to light-front quantization in ${\varphi }_2^4$ theory
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Critical behavior of the 2d scalar theory: resumming the ${\mathrm{N}}^8\mathrm{LO}$ perturbative mass gap
• RG flows on $S^d$ and Hamiltonian truncation
• Tadpoles and vacuum bubbles in light-front quantization
• Corrections to scaling in the 2D phi^4 model: Monte Carlo results and some related problems
• On computing non-equilibrium dynamics following a quench
• A First Step Towards Effectively Nonperturbative Scattering Amplitudes in the Perturbative Regime
• Nonperturbative dynamics of (2+1)d ${\varphi }^4$-theory from Hamiltonian truncation