Quantum statistics transmutation via magnetic flux attachment

Abstract

We consider a model for two types (bath and tracers) of 2D quantum particles in a perpendicular magnetic field. Interactions are short range and inter-species, and we assume that the bath particles are fermions, all lying in the lowest Landau level of the magnetic field. Heuristic arguments then indicate that, if the tracers are strongly coupled to the bath, they effectively change their quantum statistics, from bosonic to fermionic or vice-versa. We rigorously compute the energy of a natural trial state, indeed exhibiting this phenomenon of statistics transmutation. The proof involves estimates for the characteristic polynomial of the Ginibre ensemble of random matrices.

arXiv comment49 pages. Minor corrections, clarifications and updated references

References in corpus (40)

• Many-Body Physics with Ultracold Gases
• Artificial gauge potentials for neutral atoms
• Rapidly Rotating Atomic Gases
• Direct observation of anyonic braiding statistics at the $\nu$=1/3 fractional quantum Hall state
• Fractional statistics in anyon collisions
• Around the circular law
• Fluctuations of eigenvalues of random normal matrices
• Plasma Analogy and Non-Abelian Statistics for Ising-type Quantum Hall States
• Characteristic Polynomials of Complex Random Matrix Models
• Quantum Hall physics in rotating Bose-Einstein condensates
• The Ground States of Large Quantum Dots in Magnetic Fields
• Entanglement Entropy and Full Counting Statistics for $2d$-Rotating Trapped Fermions
• Emergence of fractional statistics for tracer particles in a Laughlin liquid
• Numerical study of charge and statistics of Laughlin quasi-particles
• Strongly correlated phases in rapidly rotating Bose gases
• Signatures of Fractional Exclusion Statistics in the Spectroscopy of Quantum Hall Droplets
• Fractional angular momentum in cold atom systems
• The two-dimensional Coulomb plasma: quasi-free approximation and central limit theorem
• Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics
• Quantum Hall phases and plasma analogy in rotating trapped Bose gases
• Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
• Quantum Hall states of bosons in rotating anharmonic traps
• Quantum transport properties of two-dimensional electron gases under high magnetic fields
• Microscopics of disordered two-dimensional electron gases under high magnetic fields: Equilibrium properties and dissipation in the hydrodynamic regime
• Local density for two-dimensional one-component plasma
• Maximum of the characteristic polynomial of the Ginibre ensemble
• Counting statistics for non-interacting fermions in a rotating trap
• A Quantum Impurity Model for Anyons
• Local incompressibility estimates for the Laughlin phase
• Multilayered density profile for noninteracting fermions in a rotating two-dimensional trap
• Emergence of Haldane pseudo-potentials in systems with short-range interactions
• Spectral Gaps and Incompressibility in a $\nu =1/3$ Fractional Quantum Hall System
• Local density of states in disordered two-dimensional electron gases at high magnetic field
• Incompressibility Estimates for the Laughlin Phase
• Low-complexity eigenstates of a $\nu =1/3$ fractional quantum Hall system
• Molecular Impurities as a Realization of Anyons on the Two-Sphere
• Emergent Fermi sea in a system of interacting bosons
• The Laughlin liquid in an external potential
• Holomorphic quantum Hall states in higher Landau levels
• Stability of the Laughlin phase against long-range interactions