Phases and criticality of the triangular lattice SU(N) Hofstadter-Hubbard model

TL;DR

This paper investigates the phase diagram and critical phenomena of the SU(N) Hofstadter-Hubbard model on a triangular lattice, revealing multiple quantum phases and their transitions relevant for synthetic quantum systems.

Contribution

It introduces a comprehensive analysis of phases and critical points in the SU(N) Hofstadter-Hubbard model, including the construction of a critical theory for phase transitions.

Findings

Identification of three distinct phases: quantum Hall, chiral spin liquid, valence bond solid.

Calculation of critical interaction strengths for phase transitions.

Development of a critical theory and transport behavior for continuous phase transitions.

Abstract

We report the study of phases and transitions of SU(N) Hofstadter-Hubbard model subject to commensurate magnetic field on the triangular lattice. At filling one fermion per site, for the number of fermion flavors 2 <= N <= 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 moire superlattices and cold atom platforms.