Abstract
We investigate the quantum phase transition of the $O(3)$ nonlinear $\ensuremath{\sigma}$ model without Berry phase in two spatial dimensions. Utilizing the $C{P}^{1}$ representation of the nonlinear $\ensuremath{\sigma}$ model, we obtain an effective action in terms of bosonic spinons interacting via compact $U(1)$ gauge fields. Based on the effective field theory, we find that the bosonic spinons are deconfined to emerge at the quantum critical point of the nonlinear $\ensuremath{\sigma}$ model. It is emphasized that the deconfinement of spinons is realized in the absence of Berry phase. This is in contrast to the previous study of Senthil et al. [Science 303, 1490 (2004)], where the Berry phase plays a crucial role, resulting in the deconfinement of spinons. It is the reason why the deconfinement is obtained even in the absence of the Berry phase effect that the quantum critical point is described by the $XY$ (``neutral'') fixed point, not the $IXY$ (``charged'') fixed point. The $IXY$ fixed point is shown to be unstable against instanton excitations and the instanton excitations are proliferated. At the $IXY$ fixed point it is the Berry phase effect that suppresses the instanton excitations, causing the deconfinement of spinons. On the other hand, the $XY$ fixed point is found to be stable against instanton excitations because an effective internal charge is zero at the neutral $XY$ fixed point. As a result the deconfinement of spinons occurs at the quantum critical point of the $O(3)$ nonlinear $\ensuremath{\sigma}$ model in two dimensions.
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