3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory

Lao, Bing-Xin; Rychkov, Slava

doi:10.21468/SciPostPhys.15.6.243

SciPost Physics

3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory

Bing-Xin Lao, Slava Rychkov

SciPost Phys. 15, 243 (2023) · published 18 December 2023

doi: 10.21468/SciPostPhys.15.6.243
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Abstract

We consider the transverse field Ising model in (2+1)D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a meaningful comparison to the 3D Ising CFT on $\mathbb{R}× S^2$, by including effective perturbations of the CFT Hamiltonian with a handful of local operators. This extreme example shows the power of conformal perturbation theory in understanding finite N effects in models on regularized $S^2$. Its ideal arena of application should be the recently proposed models of fuzzy sphere regularization.

TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.15.6.243
TI  - 3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory
PY  - 2023/12/18
UR  - https://scipost.org/SciPostPhys.15.6.243
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 15
IS  - 6
SP  - 243
A1  - Lao, Bing-Xin
AU  - Rychkov, Slava
AB  - We consider the transverse field Ising model in (2+1)D, putting 12 spins at the vertices of the regular icosahedron. The model is tiny by the exact diagonalization standards, and breaks rotation invariance. Yet we show that it allows a meaningful comparison to the 3D Ising CFT on $\mathbb{R}× S^2$, by including effective perturbations of the CFT Hamiltonian with a handful of local operators. This extreme example shows the power of conformal perturbation theory in understanding finite N effects in models on regularized $S^2$. Its ideal arena of application should be the recently proposed models of fuzzy sphere regularization.
ER  -

@Article{10.21468/SciPostPhys.15.6.243,
	title={{3D Ising CFT and exact diagonalization on icosahedron: The power of conformal perturbation theory}},
	author={Bing-Xin Lao and Slava Rychkov},
	journal={SciPost Phys.},
	volume={15},
	pages={243},
	year={2023},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.15.6.243},
	url={https://scipost.org/10.21468/SciPostPhys.15.6.243},
}

Cited by 6

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¹ ² Bing-Xin Lao,
¹ Slava Rychkov

Funder for the research work leading to this publication

Simons Foundation