Conformal Data for the O(3) Wilson-Fisher Conformal Field Theory from Fuzzy Sphere Realization of the Quantum Rotor...

Area of Science:

• Condensed Matter Physics
• Quantum Field Theory

Background:

• Strongly interacting fermions and internal symmetries are crucial in condensed matter.
• Understanding quantum phase transitions and universality classes is a key challenge.

Purpose of the Study:

• To present a model for O(3) symmetric fermions on the fuzzy sphere.
• To investigate quantum phase transitions within the O(3) Wilson-Fisher universality class.
• To provide a framework for accessing conformal data in O(N) Wilson-Fisher conformal field theories.

Main Methods:

• Exact diagonalization and density matrix renormalization group (DMRG).
• Conformal perturbation theory to locate quantum critical points and obtain scaling dimensions.
• Analysis of operator product expansion (OPE) coefficients.

Main Results:

• The model preserves rotational symmetry and exhibits a quantum phase transition.
• Identified 24 primary operators and determined OPE coefficients.
• A weakly irrelevant operator relevant to dimerized antiferromagnets was identified.

Conclusions:

• The study successfully models strongly interacting fermions with O(3) symmetry.
• The findings offer a quantitative method for analyzing conformal field theories.
• Results are consistent with conformal bootstrap and large quantum-number expansions.