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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• Chern number
• Chirality
• Landau levels
• Magnetic order
• Magnetism
• Nematic order
• Quantum field theory (low energy)
• Quantum spin liquid
• Spin liquid
• Triangular lattice
• Gutzwiller approximation
• Heisenberg model
• Monte Carlo methods
• Quantum Monte Carlo