Hamiltonian Truncation Crafted for UV-divergent QFTs

Abstract

We develop the theory of Hamiltonian Truncation (HT) to systematically study RG flows that require the renormalization of coupling constants. This is a necessary step towards making HT a fully general method for QFT calculations. We apply this theory to a number of QFTs defined as relevant deformations of $d=1+1$ CFTs. We investigated three examples of increasing complexity: the deformed Ising, Tricritical-Ising, and non-unitary minimal model $M(3,7)$. The first two examples provide a crosscheck of our methodologies against well established characteristics of these theories. The $M(3,7)$ CFT deformed by its $Z_2$-even operators shows an intricate phase diagram that we clarify. At a boundary of this phase diagram we show that this theory flows, in the IR, to the $M(3,5)$ CFT.

Comments: Published version with corrected typos, added footnote, 42 pages, 12 figures