Quantum Hall to Chiral Spin Liquid transition in a Triangular Lattice Hofstadter-Hubbard Model

TL;DR

This paper studies the quantum phase transition from an integer quantum Hall state to a chiral spin liquid in a triangular lattice Hofstadter-Hubbard model using DMRG, revealing critical behavior consistent with an Ising transition.

Contribution

It provides a detailed numerical analysis of the phase transition, including critical exponents and entanglement properties, in a complex lattice model with magnetic flux.

Findings

Identification of the phase transition point and critical exponents.

Observation of divergence in correlation lengths near the critical point.

Detection of gap closing in specific excitations related to the order parameter.

Abstract

We investigate the weak interaction integer quantum Hall (IQH) phase, the intermediate interaction phase identified as a chiral spin liquid (CSL) and the transition between them in the triangular lattice Hofstadter-Hubbard model at a density of one electron per site in an orbital magnetic field corresponding to one-quarter flux per plaquette. Our primary tool is the finite system density matrix renormalization group (DMRG) method with both interaction-strength scan and fixed interaction techniques for cylinders of circumference 3, 5, and 7 and lengths up to 240. For the IQH phase, we use single particle exact diagonalization to clarify finite size effects, including an excess charge on the edges of our cylinders, and the limitations of entanglement spectra degeneracies on small circumference cylinders. For both phases, we use DMRG to study the entanglement spectra, the entanglement entropy, and the effect of flux insertion on charge and spin pumping, all of which show key differences between the two phases. To study the transition, we use interaction-strength scans extending between the two phases, and apply a scaling data collapse of a bond-dimerization order parameter to extract critical exponents. We also extract critical behavior from the divergence of correlation lengths on the IQH side, measuring decay away from edges of both the dimerization order parameter and transverse edge currents. The critical behavior and exponents are consistent with an Ising transition in 1+1 dimensions. Finally, we obtain excited states in various quantum number sectors finding that the gap to a charge neutral momentum $\pi$ excitation corresponding to fluctuations of the dimerization order parameter closes in the vicinity of the critical point but gaps to other excitations remain large.