Topological Criticality with Charge-3e Fluctuations in the SU(3) Triangular-Lattice Hofstadter--Hubbard Model
Abstract
A transition between an integer quantum Hall insulator and a chiral spin liquid can become critical without closing the single-electron gap, raising the question of which composite excitations govern the change in topological order. We investigate this question in the SU(3) triangular-lattice Hofstadter--Hubbard model at one particle per site and magnetic flux π/3 per triangle. Using infinite density matrix renormalization group calculations, we identify a weak-coupling integer quantum Hall phase and an interaction-driven SU(3)1 chiral spin liquid. Near the transition, both the neutral and charge-3e correlation lengths increase substantially, whereas the single-electron correlation length remains short, providing evidence for a Chern--Simons--Higgs critical theory, where a gauge-invariant monopole carries the quantum numbers of a fermionic SU(3)-singlet trion. We discuss the implications for doping the system and recent experiments on doping ν=−2/3 fractional quantum anomalous Hall in tMoTe2.
Related
- Topological Acoustic Metamaterials with Synthetic Magnetism: Observation of Hofstadter Spectrum and Topological Edge States
- Collective Symmetry and Criticality from Single-Component Fluctuations
- Free energy fluctuations of symmetric perceptron models up to and including criticality
- Ab initio spin Hamiltonians and magnetism of Ce and Yb triangular-lattice compounds
- Active model B+ from run-and-tumble particles on a triangular lattice
BibTeX
@misc{liu2026topological,
title = {{Topological Criticality with Charge-\(3e\) Fluctuations in the \(\mathrmSU(3)\) Triangular-Lattice Hofstadter--Hubbard Model}},
author = {Yang Liu and Ya-Hui Zhang and Xue-Yang Song},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.37575},
eprint = {2610.37575},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.37575},
note = {CC BY-NC-SA 4.0},
}
RIS
TY - UNPB
TI - Topological Criticality with Charge-3e Fluctuations in the SU(3) Triangular-Lattice Hofstadter--Hubbard Model
AU - Yang Liu
AU - Ya-Hui Zhang
AU - Xue-Yang Song
PY - 2026
DA - 2026/10/27
PB - arXiv
DO - 10.48550/arxiv.2610.37575
UR - https://arxiv.org/abs/2610.37575
AB - A transition between an integer quantum Hall insulator and a chiral spin liquid can become critical without closing the single-electron gap, raising the question of which composite excitations govern the change in topological order. We investigate this question in the SU(3) triangular-lattice Hofstadter--Hubbard model at one particle per site and magnetic flux π/3 per triangle. Using infinite density matrix renormalization group calculations, we identify a weak-coupling integer quantum Hall phase and an interaction-driven SU(3)_1 chiral spin liquid. Near the transition, both the neutral and charge-3e correlation lengths increase substantially, whereas the single-electron correlation length remains short, providing evidence for a Chern--Simons--Higgs critical theory, where a gauge-invariant monopole carries the quantum numbers of a fermionic SU(3)-singlet trion. We discuss the implications for doping the system and recent experiments on doping ν=−2/3 fractional quantum anomalous Hall in tMoTe_2.
ER -