Collective field theory for quantum Hall states
Abstract
We develop a collective field theory for fractional quantum Hall (FQH) states. We show that in the leading approximation for a large number of particles, the properties of Laughlin states are captured by a Gaussian free field theory with a background charge. Gradient corrections to the Gaussian field theory arise from the covariant ultraviolet regularization of the theory, which produces the gravitational anomaly. These corrections are described by a theory closely related to the Liouville theory of quantum gravity. The field theory simplifies the computation of correlation functions in FQH states and makes manifest the effect of quantum anomalies.
 Publication:

Physical Review B
 Pub Date:
 December 2015
 DOI:
 10.1103/PhysRevB.92.235141
 arXiv:
 arXiv:1412.8716
 Bibcode:
 2015PhRvB..92w5141L
 Keywords:

 73.43.Cd;
 02.40.k;
 11.10.z;
 73.43.Lp;
 Theory and modeling;
 Geometry differential geometry and topology;
 Field theory;
 Collective excitations;
 Condensed Matter  Strongly Correlated Electrons;
 High Energy Physics  Theory;
 Mathematical Physics
 EPrint:
 v1: 20 pages