Massless excitations at $\theta =\pi$ in the $CP^{N-1}$ model with large values of $N$
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 $\theta = \pi$ 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.
- Publication:
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arXiv e-prints
- Pub Date:
- February 2006
- DOI:
- 10.48550/arXiv.cond-mat/0602653
- arXiv:
- arXiv:cond-mat/0602653
- Bibcode:
- 2006cond.mat..2653P
- Keywords:
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- Condensed Matter - Mesoscopic Systems and Quantum Hall Effect;
- Condensed Matter - Statistical Mechanics
- E-Print:
- Elsart class, 46 pages, 2 figures