Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model

TL;DR

This paper investigates the phase transition between quantum Hall and chiral spin liquid phases in a triangular lattice Hofstadter-Hubbard model using matrix product states, revealing symmetry breaking and critical fluctuations.

Contribution

It uncovers a spontaneous glide particle-hole symmetry breaking at the transition and characterizes the nature of the phase transition in finite and infinite systems.

Findings

Spontaneous symmetry breaking at the quantum Hall to spin liquid transition.

Transition exhibits algebraic long-range correlations of spin-singlet operators.

In the 2D limit, the transition is continuous with critical current fluctuations.

Abstract

Recent advances in moir\'e engineering motivate the study of lattice models of strongly-correlated electrons subjected to substantial orbital magnetic flux. We analyze the triangular lattice Hofstadter-Hubbard model at one-quarter flux quantum per plaquette and a density of one electron per site, where a chiral spin liquid phase may exist between weak-coupling integer quantum Hall and strong-coupling 120$^\circ$ antiferromagnetic phases. We use matrix product state methods and analytical arguments to investigate this model compactified to cylinders of finite circumference. We uncover a glide particle-hole symmetry operation which, we argue, is spontaneously broken at the quantum Hall to spin liquid transition on odd-circumference cylinders. We numerically verify the spontaneous symmetry breaking and further demonstrate that this transition is associated with algebraic long-range correlations of various spin-singlet, charge-neutral operators. For even-circumference cylinders, the transition becomes a crossover associated with a large correlation length that grows substantially with circumference. Our findings suggest that in the two-dimensional limit, the transition to a chiral spin liquid phase is continuous and features critical fluctuations of the current.