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arXiv:2601.14458 · Physical Review Letters

Chirality and Quasi-Long-Range Order in Finite-Flux Gutzwiller States for Magnetized Frustrated Magnets

Wen O. Wang, Urban F. P. Seifert, Oleg A. Starykh, Leon Balents

Published Jul 10, 2026• 2 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/g52b-t4cj

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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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The parton approach for quantum spin liquids gives a transparent description of low-energy elementary excitations, e.g., spinons and emergent gauge-field fluctuations. The latter ones are directly coupled to the hopping/pairing of spinons. By using the fermionic representation of the U(1)U(1)U(1) Dirac state on the kagome lattice and variational Monte Carlo techniques to include the Gutzwiller projection, we analyze the effect of modifying the gauge fields in the spinon kinematics. In particular, we construct low-energy monopole excitations, which are shown to be gapless in the thermodynamic limit. States with a finite number of monopoles or with a finite density of them are also considered, with different patterns of the gauge fluxes. We show that these chiral states are not stabilized in the Heisenberg model with nearest-neighbor superexchange couplings, and the Dirac state corresponds to the lowest-energy ansatz within this family of variational wave functions. Our results support the idea that spinons with a gapless conical spectrum coexist with gapless monopole excitations, even for the spin-1/2 case.
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Abstract We present a systematic classification and variational study of chiral quantum spin liquids on the pyrochlore lattice based on fermionic parton constructions. Focusing on chiral U ( 1 ) and Z 2 spin-liquid Ansätze , we characterize their symmetry properties, flux structures, and low-energy spinon spectra within a projective symmetry group framework, and incorporate gauge fluctuations through Gutzwiller-projected wave functions studied by variational Monte Carlo. From the equal-time spin structure factor, we develop correlation-based diagnostics that distinguish gauge-dominated Coulomb phases from states with substantial matter-field and short-range contributions. Distinct chiral flux sectors, though close in energy, exhibit markedly different degrees of emergent U ( 1 ) gauge-field dominance, reflected in the geometry and contrast of pinch-point singularities. Although these states are not competitive ground states of the nearest-neighbor Heisenberg model, they define a physically meaningful family of proximate chiral phases relevant to extended pyrochlore Hamiltonians.