Local incompressibility estimates for the Laughlin phase

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.

Version 3. Some details clarified, recent results of arXiv:1707.05059 taken into account

References in corpus (12)

• Many-Body Physics with Ultracold Gases
• Geometric methods for nonlinear many-body quantum systems
• Next Order Asymptotics and Renormalized Energy for Riesz Interactions
• Monte Carlo simulation method for Laughlin-like states in a disk geometry
• Emergence of fractional statistics for tracer particles in a Laughlin liquid
• Concentration for Coulomb gases and Coulomb transport inequalities
• Monte Carlo study of Bose Laughlin wave function for filling factors 1/2, 1/4 and 1/6
• Fractional angular momentum in cold atom systems
• Some contributions to many-body quantum mathematics
• Repulsion in low temperature $\beta$-ensembles
• The Laughlin liquid in an external potential
• Equidistribution of jellium energy for Coulomb and Riesz Interactions

Cited by in corpus (8)

• Coulomb and Riesz gases: The known and the unknown
• Floating Wigner crystal with no boundary charge fluctuations
• Emergence of Haldane pseudo-potentials in systems with short-range interactions
• Spectral Gaps and Incompressibility in a $\nu =1/3$ Fractional Quantum Hall System
• Quantum statistics transmutation via magnetic flux attachment
• The Laughlin liquid in an external potential
• Holomorphic quantum Hall states in higher Landau levels
• Stability of the Laughlin phase against long-range interactions