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Peer-reviewedCC BY 4.0SciPost Physics

Conformal data for the O(2) Wilson-Fisher CFT in (2+1)-dimensional spacetime from exact diagonalization and matrix product states on the fuzzy sphere

  • Arjun Dey1,2
  • Loic Herviou3,4
  • Christopher Mudry1,2
  • Slava Rychkov5
  • Andreas Martin Läuchli1,2
5 affiliations
  1. 1Paul Scherrer Institute
  2. 2École Polytechnique Fédérale de Lausanne
  3. 3Grenoble Alpes University
  4. 4Laboratoire de Physique et Modélisation des Milieux Condensés
  5. 5Institut des Hautes Études Scientifiques
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Abstract

We study at zero temperature a microscopic quantum spin-1 model on the fuzzy sphere that realizes the O(2) O ( 2 ) Wilson-Fisher conformal field theory (CFT) in (2+1) ( 2 + 1 ) -dimensional spacetime at a quantum critical point. Here, we use the fuzzy-sphere regularization as it preserves the full spatial SO(3) S O ( 3 ) rotational symmetry of the CFT, enabling the state-operator correspondence that maps energy eigenstates directly to CFT operators. Using exact diagonalization (ED) and matrix product state (MPS) techniques combined with conformal perturbation theory (CPT), we extract conformal data including scaling dimensions and operator product expansion (OPE) coefficients. We identify 48 primary operators and their descendants, organized by the conserved O(2) O ( 2 ) charge S^{z} S z and spatial angular momentum L L . Our numerical results for the scaling dimensions of the lowest primary operators show good agreement with conformal bootstrap predictions. We verify predictions from the large charge expansion, which provides systematic predictions for operators carrying large U(1) U ( 1 ) charge, connecting the Goldstone mode physics in the ordered phase to phonon primaries at the critical point.

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Cite

BibTeXRIS
BibTeX
@article{dey2026conformal,
  title = {{Conformal data for the $O(2)$ Wilson-Fisher CFT in $(2+1)$-dimensional spacetime from exact diagonalization and matrix product states on the fuzzy sphere}},
  author = {Arjun Dey and Loic Herviou and Christopher Mudry and Slava Rychkov and Andreas Martin Läuchli},
  journal = {SciPost Physics},
  year = {2026},
  month = oct,
  doi = {10.21468/scipostphys.21.4.094},
  url = {https://scipost.org/10.21468/SciPostPhys.21.4.094},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Conformal data for the O(2) Wilson-Fisher CFT in (2+1)-dimensional spacetime from exact diagonalization and matrix product states on the fuzzy sphere
AU  - Arjun Dey
AU  - Loic Herviou
AU  - Christopher Mudry
AU  - Slava Rychkov
AU  - Andreas Martin Läuchli
PY  - 2026
DA  - 2026/10/14
JO  - SciPost Physics
DO  - 10.21468/scipostphys.21.4.094
UR  - https://scipost.org/10.21468/SciPostPhys.21.4.094
AB  - We study at zero temperature a microscopic quantum spin-1 model on the fuzzy sphere that realizes the O(2) O ( 2 ) Wilson-Fisher conformal field theory (CFT) in (2+1) ( 2 + 1 ) -dimensional spacetime at a quantum critical point. Here, we use the fuzzy-sphere regularization as it preserves the full spatial SO(3) S O ( 3 ) rotational symmetry of the CFT, enabling the state-operator correspondence that maps energy eigenstates directly to CFT operators. Using exact diagonalization (ED) and matrix product state (MPS) techniques combined with conformal perturbation theory (CPT), we extract conformal data including scaling dimensions and operator product expansion (OPE) coefficients. We identify 48 primary operators and their descendants, organized by the conserved O(2) O ( 2 ) charge S^{z} S z and spatial angular momentum L L . Our numerical results for the scaling dimensions of the lowest primary operators show good agreement with conformal bootstrap predictions. We verify predictions from the large charge expansion, which provides systematic predictions for operators carrying large U(1) U ( 1 ) charge, connecting the Goldstone mode physics in the ordered phase to phonon primaries at the critical point.
SN  - 2542-4653
ER  -