RG flow from \({\Phi}^4\) theory to the 2D Ising model

DOI10.1007/JHEP08(2017)056zbMATH Open1381.81105arXiv1704.04500MaRDI QIDQ1700127

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Publication date: 2 March 2018

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Abstract: We study 1+1 dimensional $ph{i}^4$ 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, $mathcalC$. We use these states to express the Hamiltonian of the full interacting theory in lightcone quantization. After truncating to states with $mathcalCleqmathcal{C}_{max}$, 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.

Full work available at URL: https://arxiv.org/abs/1704.04500

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