The Laughlin liquid in an external potential
arXiv:1707.05059 · doi:10.1007/s11005-017-1020-5
Abstract
We study natural perturbations of the Laughlin state arising from the effects of trapping and disorder. These are N-particle wave functions that have the form of a product of Laughlin states and analytic functions of the N variables. We derive an upper bound to the ground state energy in a confining external potential, matching exactly a recently derived lower bound in the large N limit. Irrespective of the shape of the confining potential, this sharp upper bound can be achieved through a modification of the Laughlin function by suitably arranged quasi-holes.
Typos corrected and one remark added. To be published in Letters in Mathematical Physics
References in corpus (8)
- First order global asymptotics for confined particles with singular pair repulsion
- Rotational spectra of weakly interacting Bose-Einstein condensates
- Emergence of fractional statistics for tracer particles in a Laughlin liquid
- Monte Carlo study of Bose Laughlin wave function for filling factors 1/2, 1/4 and 1/6
- Quantum Hall phases and plasma analogy in rotating trapped Bose gases
- Quantum Hall states of bosons in rotating anharmonic traps
- Local incompressibility estimates for the Laughlin phase
- Incompressibility Estimates for the Laughlin Phase