Generalized Model Fractional Quantum Hall States on Lattices

TL;DR

This paper constructs and analyzes lattice model wave functions for various fractional quantum Hall states, advancing understanding of topological phases on lattices with potential applications in cold-atom systems.

Contribution

It introduces a systematic method to build lattice model states for Laughlin, Moore--Read, and $ ext{Z}_k$ Read--Rezayi series, highlighting their unique features and stability.

Findings

Lattice-specific states exhibit idealized energy and entanglement features.

Modified clustering behavior distinguishes lattice states from continuum counterparts.

The work provides a constructive approach for engineering topological orders in lattice systems.

Abstract

Model wave functions are essential for studying fractional quantum Hall phases, yet lattice model states have so far been limited to bosonic systems with on-site interactions. In this work, by combining analytical and numerical methods, we systematically construct lattice model states for the Laughlin, Moore--Read, and general $\mathbb{Z}_k$ Read--Rezayi series. Our lattice-specific states are characterized by their idealized energy and entanglement features and are distinguished from their continuum counterparts by a modified clustering behavior. Our theory advances the understanding of the stability of topologically ordered phases and illustrates the organizing principles of the conformal Hilbert space on lattices. Practically, this work paves the way for further studying lattice-specific excitations and offers a constructive route for engineering topological orders within density interactions, with potential immediate implications for cold-atom and synthetic flat-band platforms.