Abstract
We defend the Fock-space Hamiltonian truncation method, which allows to calculate numerically the spectrum of strongly coupled quantum field theories, by putting them in a finite volume and imposing a UV cutoff. The accuracy of the method is improved via an analytic renormalization procedure inspired by the usual effective field theory. As an application, we study the two-dimensional Phi^4 theory for a wide range of couplings. The theory exhibits a quantum phase transition between the symmetry-preserving and symmetry-breaking phases. We extract quantitative predictions for the spectrum and the critical coupling and make contact with previous results from the literature. Future directions to further improve the accuracy of the method and enlarge its scope of applications are outlined.
Highlights
How do we extract predictions about a strongly coupled quantum field theory (QFT) which is not exactly solvable? The lattice would be one answer, but it is not the only one
The advances reported in this paper, as well as the ongoing progress in developing the other variants of the Hamiltonian truncation [9,10,11], [12,13,14] make us hopeful that in a not too distant future these methods will turn into precision tools for studying strongly coupled QFTs
One difference is that their method is perturbative, unlike our basic equation (3.6) which is all order in ΔH. Another difference is that stochastic error correction (SEC) computes infinite sums involved in the definition of ΔH via Monte Carlo sampling, while we found an analytic approximation for this correction term
Summary
How do we extract predictions about a strongly coupled quantum field theory (QFT) which is not exactly solvable? The lattice would be one answer, but it is not the only one. Hamiltonian truncation techniques, which generalize the Rayleigh-Ritz method familiar from quantum mechanics, are a viable deterministic alternative to the lattice Monte Carlo (MC) simulations, at least for some theories. These techniques remain insufficiently explored, compared to the lattice, and their true range of applicability may be much wider than what is currently believed. The advances reported in this paper, as well as the ongoing progress in developing the other variants of the Hamiltonian truncation [9,10,11], [12,13,14] make us hopeful that in a not too distant future these methods will turn into precision tools for studying strongly coupled QFTs. The structure of the paper is clear from the table of contents.
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