Abstract
We prove sharp density upper bounds on optimal length-scales for the ground states of classical 2D Coulomb systems and generalizations thereof. Our method is new, based on an auxiliary Thomas–Fermi-like variational model. Moreover, we deduce density upper bounds for the related low-temperature Gibbs states. Our motivation comes from fractional quantum Hall physics, more precisely, the perturbation of the Laughlin state by external potentials or impurities. These give rise to a class of many-body wave-functions that have the form of a product of the Laughlin state and an analytic function of many variables. This class is related via Laughlin’s plasma analogy to Gibbs states of the generalized classical Coulomb systems we consider. Our main result shows that the perturbation of the Laughlin state cannot increase the particle density anywhere, with implications for the response of FQHE systems to external perturbations.
Highlights
The fractional quantum Hall effect (FQHE) [25,29,33,69] is a remarkable feature of the transport properties of 2D electron gases under strong perpendicular magnetic fields and at low temperatures
We prove sharp density upper bounds on optimal length-scales for the ground states of classical 2D Coulomb systems and generalizations thereof
Our motivation comes from fractional quantum Hall physics, more precisely, the perturbation of the Laughlin state by external potentials or impurities
Summary
The fractional quantum Hall effect (FQHE) [25,29,33,69] is a remarkable feature of the transport properties of 2D electron gases under strong perpendicular magnetic fields and at low temperatures. Soon after its experimental discovery [71], it was recognized in the seminal works of Laughlin [31,32] that the origin of the effect lies in the emergence of a new, strongly correlated, phase of matter The latter has been argued to host elementary excitations with fractional charge, a fact that was later experimentally confirmed [21,47,63]. But still lacking an experimental confirmation, is the possibility that these excitations (quasi-particles) are anyons [6,45,73], i.e. have quantum statistics different from those of bosons and fermions, the only known types of fundamental particles Due to these exciting prospects, it is an ongoing quest in condensed matter physics to generalize FQHE physics to other, more flexible, contexts than the 2D electron gas [9,11,20,49,72]. Their energy is separated from the rest of the spectrum by a gap independent of volume and particle number
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