We report the study of phases and transitions of the $\text{SU}\left(N\right)$ Hofstadter-Hubbard model subject to a commensurate magnetic field on the triangular lattice. At filling one fermion per site, for the number of fermion flavors $2\le N\le 8$, we identify three distinct phases and calculate critical interaction strength from parton large-$N$ mean-field approximation. Integer quantum Hall, chiral spin liquid, and valence bond solid states could be realized upon varying the Hubbard interaction $U$ and the number of flavor $N$. We construct the critical theory for the putative continuous transition from quantum Hall states to chiral spin liquid and calculate the critical transport behavior using quantum Boltzmann equations for general $N$. These results could be validated in synthetic systems such as moiré superlattices and cold atom platforms.

Close

PrevNext

View figure in article

• Large-N expansion in field theory
• Quantum criticality
• Spin liquid
• Strongly correlated systems
• Boltzmann theory
• Chern-Simons gauge theory
• Mean field theory