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Anyon Dispersion from Nonuniform Magnetic Field on the Sphere
Mina-Lou Schleith1,2,3, Tomohiro Soejima1,4,5, Eslam Khalaf1
1Harvard University, Department of Physics, Cambridge, Massachusetts 02138, USA.
Physical Review Letters
|August 10, 2026
Summary
We present a model for itinerant anyons in a nonuniform magnetic field, enabling the study of their dispersion. This work offers an exactly solvable mechanism for interaction-induced anyon dispersion without single-particle hopping.
Area of Science:
- Condensed Matter Physics
- Quantum Field Theory
- Topological Phases of Matter
Background:
- Fractional quantum anomalous Hall states in moiré systems suggest itinerant anyon phases.
- Mobility of anyons requires the absence of continuous magnetic translation symmetry (CMTS).
- CMTS on a sphere is analogous to SU(2) rotation symmetry.
Purpose of the Study:
- To investigate anyons on a sphere with a nonuniform magnetic field breaking SU(2) to U(1) symmetry.
- To study the energy dispersion of anyons as a function of angular momentum.
- To provide an exactly solvable model for interaction-induced anyon dispersion.
Main Methods:
- Utilized a nonuniform magnetic field concentrating at sphere poles, parametrized by R.
- Established an exact mapping for p-body correlation functions of Laughlin quasiholes.
- Analytically computed the interaction-generated potential and derived anyon dispersion.
Main Results:
- The nonuniform field allows study of anyon dispersion while maintaining flat single-particle bands.
- An exact mapping relates correlation functions in nonuniform and uniform fields.
- A static potential alone generates anyon dispersion via emergent magnetic fields and many-body Berry phase.
Conclusions:
- Demonstrated an exactly solvable realization of interaction-induced anyon dispersion.
- The mechanism converts symmetry-breaking potential into kinetic energy without single-particle dispersion or hopping.
- The derived anyon dispersion describes azimuthal motion analogous to spin precession.
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