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Emergent Gauge Flux in Mixed QED3 with Flavor Chemical Potential: Implications for Magnetized U(1) Dirac Spin Liquids

Chuang Chen1,2, Urban F. P. Seifert3, Kexin Feng1,2, Oleg A. Starykh4, Leon Balents5,6,7, and Zi Yang Meng1,2,*

  • *Contact author: zymeng@hku.hk
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Phys. Rev. X 16, 041029 – Published 30 October, 2026

DOI: https://doi.org/10.1103/yb9y-3t91

Abstract

We design a lattice model of a “mixed” U(1) gauge field coupled to fermions with a flavor chemical potential and solve it with large-scale determinant quantum Monte Carlo simulations. In this mixed construction, dynamical magnetic monopole events are suppressed in the temporal-continuum limit. For zero flavor chemical potential, the model realizes three-dimensional quantum electrodynamics (QED3) which has been argued to describe the ground state and low-energy excitations of the Dirac spin liquid phase of quantum antiferromagnets. At finite flavor chemical potential, which corresponds to a Zeeman field perturbing the Dirac spin liquid, we find a “chiral flux” phase which is characterized by the generation of a finite mean emergent gauge flux and, accordingly, the formation of relativistic Landau levels for the Dirac fermions. We use field-theory arguments to argue that in this state a U(1)m magnetic symmetry is spontaneously broken, leading to a gapless photon mode. Because of spin-flux attachment this mode would contribute to the low-energy longitudinal spin response. We numerically compute longitudinal and transverse spin structure factors which match our continuum and lattice mean-field theory predictions. In a different region of the phase diagram, strong fluctuations of the emergent gauge field give rise to an antiferromagnetically ordered state with gapped Dirac fermions coexisting with a deconfined gauge field. We also find an interesting intermediate phase where the chiral flux phase and the antiferromagnetic phase coexist. We argue that our results pave the way to testable predictions for magnetized Dirac spin liquids in frustrated quantum antiferromagnets.

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Dirac spin liquids are intriguing states of matter characterized by fractionalized excitations, with their low-energy physics described by a strongly interacting emergent gauge theory. How this fractionalization and the emergent gauge dynamics manifest themselves in response to an external magnetic field has remained challenging. We performed large-scale quantum Monte Carlo simulations and field-theoretic analyses of a quantum lattice model of fermionic spinons subject to an applied flavor chemical potential corresponding to a Zeeman magnetic field. We identified a chiral flux phase, in which the system spontaneously generates a net emergent gauge flux, and neighboring antiferromagnetic and coexisting phases within the global phase diagram. In the chiral flux phase, the spectrum of Dirac spinons is organized into relativistic Landau levels. Our numerical calculations exhibit signatures of a gapless excitation that we argue to be consistent with the photon mode of the emergent gauge field predicted by field theory. Our work provides concrete dynamical spin structure factor predictions, establishing neutron scattering signatures to detect emergent gauge fields and fractionalization in frustrated magnets.

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Phys. Rev. X 16, 041029– Published 30 October, 2026
  • Received 21 August 2025
  • Revised 6 August 2026
  • Accepted 28 September 2026
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