Crystallization in the Fractional Quantum Hall Regime with Disorder-Aware Neural Quantum States

TL;DR

This paper uses neural-network variational Monte Carlo with disorder-aware neural quantum states to demonstrate and analyze Wigner crystal phases in fractional quantum Hall systems, revealing a unified phase diagram and asymmetry in crystallization.

Contribution

It introduces a novel neural-network variational approach that captures both fractional quantum Hall liquids and Wigner crystals within a single framework, uncovering new phase relationships.

Findings

First microscopic demonstration of a disorder-pinned hole Wigner crystal.

Identification of a crossover connecting hole and electron Wigner crystals.

Establishment of a phase diagram showing asymmetry in crystallization near different filling factors.

Abstract

We present the first microscopic demonstration of a disorder-pinned hole Wigner crystal (WC), providing a natural explanation for the reentrant integer quantum Hall effect observed near $\nu=2/3$, as well as its analogs in fractional Chern insulators. We further identify a novel crossover regime above filling $\nu=2/3$ that connects this hole WC to an electron WC, characterized by a network-like electron density structure. To uncover these phenomena, we use neural-network variational Monte Carlo (NNVMC) with a disorder-aware self-attention neural quantum state that describes both fractional quantum Hall (FQH) liquids and Wigner crystals within a single unbiased variational framework. More broadly, our method establishes a unified phase diagram that exposes a fundamental asymmetry in crystallization across half-filling: near $\nu=1/3$, increasing LL mixing and disorder both stabilize an electron WC, whereas near $\nu=2/3$, the hole WC dominates at weak LL mixing and ultimately gives way to the electron WC at strong LL mixing.