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arXiv · 2406.15348

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

Stefan Divic·Tomohiro Soejima·Valentin Crépel·Michael P. Zaletel·Andrew Millis
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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.

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Stefan Divic, Tomohiro Soejima, Valentin Crépel, Michael P. Zaletel, Andrew Millis. 2024-06-21. Chiral Spin Liquid and Quantum Phase Transition in the Triangular Lattice Hofstadter-Hubbard Model. https://doi.org/10.1103/g84x-qwrk

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