Liouville perturbation theory for Laughlin state and Coulomb gas

Abstract

We consider the generating functional (logarithm of the normalization factor) of the Laughlin state on a sphere, in the limit of a large number of particles N. The problem is reformulated in terms of a perturbative expansion of a 2d QFT, resembling the Liouville field theory. We develop an analog of the Liouville loop perturbation theory, which allows us to quantitatively study the generating functional for an arbitrary smooth metric and an inhomogeneous magnetic field beyond the leading orders in large N.

Coulomb and Riesz gases: The known and the unknown

“…342, 343, 423, and 425. A different line of research is to study the properties of Laughlin states on Riemann surfaces 242,297,298,381 or to interpret the different terms in the large-N expansion of the Coulomb gas free energy in an external potential as geometric quantities 509 . The 2D Coulomb gas appears in a variety of other situations with a geometric content, for instance in the study of the determinant of the Laplace-Beltrami operator on surfaces 391 .…”

Coulomb and Riesz gases: The known and the unknown

“…311, 312, and 387. A different line of research is to study the properties of Laughlin states on Riemann surfaces 219,266,267,347 or to interpret the different terms in the large-N expansion of the Coulomb gas free energy in an external potential as geometric quantities 455 . The 2D Coulomb gas appears in a variety of other situations with a geometric content, for instance in the study of the determinant of the Laplace-Beltrami operator on surfaces 356 .…”