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Four-dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msup><mml:mrow><mml:mtext>CP</mml:mtext></mml:mrow><mml:mn>1</mml:mn></mml:msup><mml:mo>+</mml:mo><mml:mi mathvariant="normal">U</mml:mi><mml:mrow><mml:mo>(</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:mrow></mml:math>lattice gauge theory for three-dimensional antiferromagnets: Phase structure, gauge bosons, and spin liquid
In this paper we study the lattice ${\text{CP}}^{1}$ model in $(3+1)$ dimensions coupled with a dynamical compact $\mathrm{U}(1)$ gauge field. This model is an effective field theory of the $s=\frac{1}{2}$ antiferromagnetic Heisenberg spin model in three spatial dimensions at zero temperature. By means of Monte Carlo simulations, we investigate its …