Gauge theories form a large class of interacting conformal field theories in 3D, among which critical Chern-Simons-matter theories play a prominent role. Here, we study a simple instance: a gapless complex scalar coupled to a $\mathrm{U}(1{)}_2$ Chern-Simons gauge field. This theory is conjectured to be dual to three other Chern-Simons-matter theories and to describe the transition between a Kalmeyer-Laughlin chiral spin liquid (a $\nu =1/2$ bosonic Laughlin state) and a trivially gapped phase. Using the fuzzy-sphere regularization, we realize the corresponding quantum phase transition between a ${\nu }_f=2$ fermionic integer quantum Hall state and a ${\nu }_b=1/2$ bosonic fractional quantum Hall state. We show that the transition is continuous and governed by a conformal field theory with $SO(3)$ global symmetry. The operator spectrum contains only one relevant Lorentz scalar, the SO(3) singlet with scaling dimension ${\mathrm{\Delta }}_S=1.52(18)$, which tunes the transition. Our nonperturbative results identify the universality class naturally associated with the $\mathrm{U}(1{)}_2$ Chern-Simons-Higgs theory and show that the conjectured dualities remain self-consistent.

Close

PrevNext

View figure in article

• Chern-Simons gauge theory
• Conformal field theory
• Fractional quantum Hall effect
• Quantum field theory
• Quantum phase transitions
• Quantum many-body systems
• Strongly correlated systems
• Exact diagonalization