Fractional quantum Hall phases of bosons with tunable interactions: From the Laughlin liquid to a fractional Wigner crystal

TL;DR

This paper investigates the phase diagram of bosonic systems in the lowest Landau level at half-filling, revealing transitions from Laughlin liquids to various crystalline phases driven by tunable interactions, including a novel fractional Wigner crystal.

Contribution

It demonstrates how specific interaction potentials, realizable with Rydberg-dressed atoms, induce new crystalline phases in fractional quantum Hall systems, expanding understanding of topological and symmetry-breaking coexistence.

Findings

Identification of a fractional Wigner crystal phase at half-filling.

Transition from Laughlin liquid to crystalline phases driven by interaction shape.

Proposal to realize these interactions using Rydberg-dressed cold atoms.

Abstract

Highly tunable platforms for realizing topological phases of matter are emerging from atomic and photonic systems, and offer the prospect of designing interactions between particles. The shape of the potential, besides playing an important role in the competition between different fractional quantum Hall phases, can also trigger the transition to symmetry-broken phases, or even to phases where topological and symmetry-breaking order coexist. Here, we explore the phase diagram of an interacting bosonic model in the lowest Landau level at half-filling as two-body interactions are tuned. Apart from the well-known Laughlin liquid, Wigner crystal phase, stripe, and bubble phases, we also find evidence of a phase that exhibits crystalline order at fractional filling per crystal site. The Laughlin liquid transits into this phase when pairs of bosons strongly repel each other at relative angular momentum $4\hbar$. We show that such interactions can be achieved by dressing ground-state cold atoms with multiple different-parity Rydberg states.