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arXiv:2601.12898 · Physical Review Letters

Emergent Gauge Flux and Spin Ordering in Magnetized Triangular Spin Liquids: Applications to Hofstadter-Hubbard Model

Jiahao Yang, Hao Tian, Si-Yu Pan, Gang Chen

Published Aug 11, 2026• 0 citations
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Abstract

Motivated by recent progress in moiré superlattices and spin-1/2 triangular-lattice antiferromagnets, we study how orbital magnetic flux and Zeeman coupling compete or cooperate in generating internal U(1) gauge flux in a triangular spin liquid. We show that orbital flux favors a chiral spin liquid with staggered internal flux, whereas Zeeman coupling destabilizes the spinon Fermi-pocket state toward a Landau-level state with spontaneous uniform internal flux and conical spin order. We demonstrate this mechanism in a spin-1/2 J_{1}-J_{2}-J_{χ} model and further identify thermal Hall and magnetic signatures that distinguish these regimes, with potential applications to moiré Hofstadter-Hubbard systems and triangular-lattice antiferromagnets.

DOI
10.1103/gbnt-vmns

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Motivated by recent progress in moiré superlattices and spin-1/2 triangular-lattice antiferromagnets, we study how orbital magnetic flux and Zeeman coupling compete or cooperate in generating internal U(1) gauge flux in a triangular spin liquid. We show that orbital flux favors a chiral spin liquid with staggered internal flux, whereas Zeeman coupling destabilizes the spinon Fermi-pocket state toward a Landau-level state with spontaneous uniform internal flux and conical spin order. We demonstrate this mechanism in a spin-1/2 J_{1}-J_{2}-J_{χ} model and further identify thermal Hall and magnetic signatures that distinguish these regimes, with potential applications to moiré Hofstadter-Hubbard systems and triangular-lattice antiferromagnets.
Recent advances in moiré 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.
We study Gutzwiller-projected wave functions for triangular-lattice U(1) Dirac spin liquids in a Zeeman field, where we allow the U(1) gauge field to develop a gauge flux, resulting in (spin-split) spinon Landau levels. We find that at a given magnetization, the optimal candidate state has a finite flux chosen such that the spinon filling lies in a |C|=1 Landau-level gap: it gives the lowest variational energy and the smallest energy variance within our correlation-matrix reconstruction for local Heisenberg-type models. By symmetry, we argue that the finite gauge flux results in a nonzero (staggered) scalar spin chirality, as also numerically observed, and further find that the |C|=1 state exhibits dominant quasi-long-ranged 120° magnetic correlations. Studying the next-to-optimal wave function with a |C|=2 Landau-level gap, we observe unusual spin-nematic correlations. Our results may provide guidance for analyzing the magnetic-field response of Dirac spin liquid candidate materials and offer numerical diagnostics that can connect to the underlying theory of spinons coupled to an emergent U(1) gauge field.
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Twisted transition metal dichalcogenides offer an exceptionally tunable moiré platform for studying correlation physics beyond conventional condensed matter systems. In particular, the intriguing interplay between the displacement field and the twist angle remains to be fully resolved. In this paper, we use large-scale density matrix renormalization group simulations to study the minimal moiré Hubbard model on a triangular lattice at half-filling, where the displacement field effect is captured by a spin-dependent staggered flux. We find that the displacement field significantly enriches the triangular Hubbard phase diagram in several qualitative ways. It rapidly destabilizes the chiral spin liquid phase beyond a narrow weak-field regime, induces pronounced chiral correlations in the strong-coupling 120∘120^\circ120∘-antiferromagnetic phase, and stabilizes incommensurate spin-density wave phases at weaker coupling. We further find signatures of a continuous transition between the chiral spin liquid and chiral antiferromagnetic phases at a finite displacement field, potentially driven by spinon condensation. Our results uncover rich displacement-field-driven many-body physics and provide useful guidance for future experiments in moiré superlattice systems.
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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.