Hamiltonian Truncation Crafted for UV-divergent QFTs

• Published in: arXiv.org
• Main Authors: Delouche, Olivier, Joan Elias Miro, Ingoldby, James
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 07.05.2024
• Subjects: Deformation; Ising model; Phase diagrams; Physics - High Energy Physics - Lattice; Physics - High Energy Physics - Phenomenology; Physics - High Energy Physics - Theory; Physics - Statistical Mechanics
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2312.09221

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.