Topological phases in small quantum Hall samples

Abstract

Topological order has proven a useful concept to describe quantum phase transitions which are not captured by the Ginzburg-Landau type of symmetry-breaking order. However, lacking a local order parameter, topological order is hard to detect. One way to detect is via direct observation of anyonic properties of excitations which are usually discussed in the thermodynamic limit, but so far has not been realized in macroscopic quantum Hall samples. Here we consider a system of few interacting bosons subjected to the lowest Landau level by a gauge potential, and theoretically investigate vortex excitations in order to identify topological properties of different ground states. Our investigation demonstrates that even in surprisingly small systems anyonic properties are able to characterize the topological order. In addition, focusing on a system in the Laughlin state, we study the robustness of its anyonic behavior in the presence of tunable finite-range interactions acting as a perturbation. A clear signal of a transition to a different state is reflected by the system's anyonic properties.

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Cited by in corpus (15)

• Chains with loops - synthetic magnetic fluxes and topological order in one-dimensional spin systems
• Signatures of Fractional Exclusion Statistics in the Spectroscopy of Quantum Hall Droplets
• Time-of-Flight Measurements as a Possible Method to Observe Anyonic Statistics
• Creating and manipulating non-Abelian anyons in cold atom systems using auxiliary bosons
• Measurable signatures of bosonic fractional Chern insulator states and their fractional excitations in a quantum-gas microscope
• Bosonic fractional quantum Hall states in driven optical lattices
• Tracing non-Abelian anyons via impurity particles
• Fractional angular momentum and anyon statistics of impurities in Laughlin liquids
• Quantum simulation of conductivity plateaux and fractional quantum Hall effect using ultracold atoms
• Quasimomentum distribution and expansion of an anyonic gas
• Fragility of the Laughlin state in an anharmonically-trapped Bose-Einstein condensate
• Ground and Low-Lying Collective States of Rotating Three-Boson System
• Strongly correlated states of trapped ultracold fermions in deformed Landau levels
• Transition from the mean-field to the bosonic Laughlin state in a rotating Bose-Einstein condensate
• Staircase in magnetization and entanglement entropy of spin squeezed condensates