Fractional Quantum Hall Effect from Frustration-Free Hamiltonians

Area of Science:

• Condensed Matter Physics
• Quantum Hall Effect
• Topological Phases

Background:

• The fractional quantum Hall effect (FQH) describes complex behaviors in 2D electron systems under strong magnetic fields.
• Realizing exotic non-Abelian topological phases is crucial for fault-tolerant quantum computing.

Purpose of the Study:

• To introduce an emergent lattice description for continuous FQH systems.
• To demonstrate how this lattice framework facilitates the control of few-body interactions.
• To explore its potential for realizing non-Abelian quantum fluids.

Main Methods:

• Development of a generalized set of few-body coherent states.
• Equivalence established between FQH Hamiltonians and a real-space von Neumann lattice of local projection operators.
• Analytical derivation of tuning one-body potentials to control pseudopotentials.

Main Results:

• An emergent lattice description for continuous FQH systems is established.
• Tuning local potentials is shown to be equivalent to tuning few-body pseudopotentials.
• The framework allows for the realization of pure few-body pseudopotentials, crucial for non-Abelian phases.

Conclusions:

• The proposed lattice description provides a novel pathway for stabilizing exotic non-Abelian topological phases, such as the Moore-Read and Fibonacci states.
• This reformulation of the FQH effect offers new avenues for rigorously proving the incompressibility of microscopic Hamiltonians.