Multi-target density matrix renormalization group for 3D CFTs on the fuzzy sphere

Abstract: The fuzzy sphere regularization provides a powerful framework for studying three-dimensional (3D) conformal field theories (CFTs) by mapping them onto numerically tractable lattice models on the spherical lowest Landau level. However, the system sizes accessible to this method have been limited by the exact diagonalization (ED). In this work, we transcend this limitation by combining the fuzzy sphere regularization with a sophisticated multi-target density matrix renormalization group (DMRG) algorithm. Focusing on the 3D Ising-type model on the spherical lowest Landau level, we calculate the 24 low-lying energies at a larger system size than previously feasible with ED. At criticality, we extract the scaling dimensions of six primary operators, and the results show significantly improved agreement with bootstrap benchmarks compared to previous ED results at smaller sizes. Our approach allows us to efficiently target multiple excited states in larger systems beyond the reach of exact diagonalization. This study establishes the fuzzy sphere regularization combined with advanced DMRG techniques as a powerful and general framework for precision physics in 3D CFTs.