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

A. M. M. Pruisken; I. S. Burmistrov; R. Shankar

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

A. M. M. Pruisken·I. S. Burmistrov·R. Shankar

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Abstract

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 $θ= π$ 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 $ν=1/2$, exact expressions for the $β$ functions. These expressions unequivocally demonstrate that the large $N$ expansion with varying $θ$ displays all the fundamental features of the quantum Hall effect.

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A. M. M. Pruisken, I. S. Burmistrov, R. Shankar. 2006-02-28. Massless excitations at $θ=π$ in the $CP^{N-1}$ model with large values of $N$. https://arxiv.org/abs/cond-mat/0602653

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