Deconfinement of Spinons on Critical Points: Multi-Flavor CP${}^1$ + U(1) Lattice Gauge Theory in Three Dimensions

Abstract

In this paper, we study the 3D $N_{\mathrm{f}}$-flavor CP${}^1$ model (a set of $N_{\mathrm{f}}$ CP${}^1$ variables) coupled with a dynamical compact U(1) gauge field by means of Monte-Carlo simulations. This model is relevant to 2D $s=1/2$ quantum spin models, and has a phase transition line which separates an ordered phase of global spin symmetry from a disordered one. From gauge theoretical point of view, the ordered phase is a Higgs phase whereas the disordered phase is a confinement phase. We are interested in the gauge dynamics just on the critical line, in particular, whether a Coulomb-like deconfinement phase is realized there. This problem is quite important to clarify low-energy excitations in certain class of quantum spin models. If the gauge dynamics is in the deconfinement phase there, spinons, which transform in the fundamental representation of the SU($N_{\mathrm{f}}$) symmetry, appear as low-energy excitations. By Monte-Carlo simulations, we found that the "phase structure" on the {\em criticality} strongly depends on the value of $N_{\mathrm{f}}$. For small $N_{\mathrm{f}}$, the confinement phase is realized, whereas the deconfinement phase appears for sufficient large $N_{\mathrm{f}}\ge 14$. This result strongly suggests that compact QED${}_3$ is in a deconfinement phase for sufficiently large number of flavors of massless fermions.

minor changes

References in corpus (3)

• "Deconfined" quantum critical points
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids

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• Quantum critical scaling behavior of deconfined spinons
• Large-N estimates of universal amplitudes of the CP^{N-1} theory and comparison with the JQ model
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