Hamiltonian truncation crafted for UV-divergent QFTs

Delouche, Olivier; Elias Miro, Joan; Ingoldby, James

doi:10.21468/SciPostPhys.16.4.105

SciPost Physics

Hamiltonian truncation crafted for UV-divergent QFTs

Olivier Delouche, Joan Elias Miro, James Ingoldby

SciPost Phys. 16, 105 (2024) · published 19 April 2024

doi: 10.21468/SciPostPhys.16.4.105
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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 $\mathbb{Z}_2$-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.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.16.4.105
TI  - Hamiltonian truncation crafted for UV-divergent QFTs
PY  - 2024/04/19
UR  - https://www.scipost.org/SciPostPhys.16.4.105
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 16
IS  - 4
SP  - 105
A1  - Delouche, Olivier
AU  - Elias Miro, Joan
AU  - Ingoldby, James
AB  - 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 $\mathbb{Z}_2$-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.
ER  -

@Article{10.21468/SciPostPhys.16.4.105,
	title={{Hamiltonian truncation crafted for UV-divergent QFTs}},
	author={Olivier Delouche and Joan Elias Miro and James Ingoldby},
	journal={SciPost Phys.},
	volume={16},
	pages={105},
	year={2024},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.16.4.105},
	url={https://scipost.org/10.21468/SciPostPhys.16.4.105},
}

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Funder for the research work leading to this publication

European Research Council [ERC]