Long-Distance Universality of Laughlin State and Calogero-Sutherland Model

Abstract

We study the universal long-distance behaviour of the Laughlin state for the fractional quantum Hall effect and the ground state of the Calogero-Sutherland model (one dimensional $1/r^2$ interaction model). In particular, it is shown that these two wave functions coincide exactly when Laughlin state is confined in a narrow cylinder geometry. The seeming difference of dimensionality is merely a difference of representation of wave functions. We also give a recipe to interpret operators acting on states in the lowest Landau level in terms of the usual one dimensional Fermion operators, which is important for extracting the Tomonaga-Luttinger liquid behaviour of the edge states.

20, UT-676

Cited by in corpus (5)

• Collective Field Theory of the Fractional Quantum Hall Edge State and the Calogero-Sutherland Model
• Exact operator bosonization of finite number of fermions in one space dimension
• The $W_{1+\infty }$ effective theory of the Calogero- Sutherland model and Luttinger systems.
• Quantum fluctuations of the Chern-Simons theory and dynamical dimensional reduction
• On the Jastrow Wave Function for N-Particles on a Plane