Four-dimensional CP${}^1+$ U(1) lattice gauge theory for 3D antiferromagnets: Phase structure, gauge bosons and spin liquid

Abstract

In this paper we study the lattice CP${}^1$ model in (3+1) dimensions coupled with a dynamical compact 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. By means of Monte Carlo simulations, we investigate its phase structure. There exist the Higgs, Coulomb and confinement phases, and the parameter regions of these phases are clarified. We also measure magnetization of O(3) spins, energy gap of spin excitations, and mass of gauge boson. Then we discuss the relationship between these three phases and magnetic properties of the high-$T_{\mathrm{c}}$ cuprates, in particular the possibility of deconfined-spinon phase. Effect of dimer-like spin exchange coupling and ring-exchange coupling is also studied.

arXiv comment4pages, 10 figures

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• Antiferromagnetic, metal-insulator, and superconducting phase transitions in underdoped cuprates: Slave-fermion t-J model in the hopping expansion
• Bosonic t-J Model in a stacked triangular lattice and its phase diagram
• Phase structure of $Z_2$ gauge theories for frustrated antiferromagnets in two dimensions
• Phase Structure of Anisotropic Antiferromagnetic Heisenberg Model on Layered Triangular Lattice: Spiral State and Deconfined Spin Liquid
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