Phase diagram and crystal melting of helium-4 in two dimensions

TL;DR

This study uses neural quantum states and variational Monte Carlo to map the zero-temperature phase diagram of two-dimensional helium-4, revealing a first-order liquid-solid transition and evidence of an intermediate hexatic phase with unique entanglement properties.

Contribution

It introduces a unified variational approach to explore liquid, solid, and intermediate phases of 2D helium-4, including the first observation of a hexatic phase in this context.

Findings

Identified a first-order liquid-solid phase transition.

Detected a possible intermediate hexatic phase with coexisting order.

Observed a sharp decrease in entanglement entropy at freezing.

Abstract

We study the zero-temperature phase diagram of two-dimensional helium-4 using neural quantum states. Our variational description allows us to address liquid and solid phases using the same functional form as well as exploring possible melting scenarios, for instance via an intermediate hexatic phase. Notably, this is achieved by performing fixed pressure variational Monte Carlo calculations. Within the isobaric ensemble framework, we are able to clearly identify the first-order liquid-solid phase transition. However, in an intermediate region of nearly constant pressure, we find that simulations of $N=30$ atoms continuously transition from liquid to solid, with signatures of a hexatic order coexisting with a small condensate fraction. Calculations for larger systems follow the metastable liquid and solid branches in this transient region. We additionally compute the R\'enyi-2 entanglement entropy across the liquid-solid phase transition and find a sharp decrease upon freezing.