Massless excitations at $θ=π$ in the $CP^{N-1}$ model with large values of $N$

Details Massless excitations at $θ=π$ in the $CP^{N-1}$ model with large values of $N$ Massless excitations at $θ=π$ in the $CP^{N-1}$ model with large values of $N$

2006-02-28

arxiv.org/abs/cond-mat/0602653v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Elsart class, 46 pages, 2 figures

Scientific paper

We study the instanton vacuum of the $CP^{N-1}$ model with large values of $N$ in 1+1 space-time dimensions. Unlike the longstanding claims which state that the theory always has a mass gap, we for the first time establish a complete {\em critical} theory for the transition at $\theta = \pi$ obtained from a mapping onto the low temperature phase of the 1D Ising model. We derive a simple effective field theory in terms of 1D massless chiral fermions. Our results include, besides a diverging correlation length with an exponent $\nu=1/2$, exact expressions for the $\beta$ functions. These expressions unequivocally demonstrate that the large $N$ expansion with varying $\theta$ displays all the fundamental features of the quantum Hall effect.

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