Massless excitations at $\theta =\pi$ in the $CP^{N1}$ model with large values of $N$
Abstract
We study the instanton vacuum of the $CP^{N1}$ model with large values of $N$ in 1+1 spacetime 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:

arXiv eprints
 Pub Date:
 February 2006
 DOI:
 10.48550/arXiv.condmat/0602653
 arXiv:
 arXiv:condmat/0602653
 Bibcode:
 2006cond.mat..2653P
 Keywords:

 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Condensed Matter  Statistical Mechanics
 EPrint:
 Elsart class, 46 pages, 2 figures