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arXiv:2412.05332 · Physical Review Letters

Phase Diagram and Crystal Melting of Helium-4 in Two Dimensions

David Linteau, Gabriel Pescia, Jannes Nys, Giuseppe Carleo, Markus Holzmann

Published May 21, 2025• 3 citations
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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. We additionally compute the Rényi-2 entanglement entropy across the liquid-solid phase transition and find a sharp decrease upon freezing. Calculations for larger systems follow the metastable liquid and solid branches in the transient region, while signatures of a hexatic order coexisting with a small condensate fraction are observed only for smaller systems as a finite-size effect.

DOI
10.1103/v1g7-m9k4

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The supersolid phase of soft-core bosons in two dimensions is investigated using the self-consistent Hartree-Fock and quantum Monte Carlo methods. An approximate phase diagram at finite temperatures is initially constructed using the mean-field approach, which is subsequently validated through precise path-integral simulations, enabling a microscopic characterization of the various phases. Superfluid and melting/freezing transitions are analyzed through the superfluid density and the long-range behavior of correlation functions associated with positional and orientational order, in accordance with the general picture of Berezinskii-Kosterlitz-Thouless transitions. A broad region at low temperatures is identified where the supersolid phase exists, separating the uniform superfluid phase from the normal quasicrystal phase. Additionally, a potential intermediate hexatic phase with quasi-long-range orientational order is identified in a narrow region between the normal solid and fluid phases. These findings establish self-consistent Hartree-Fock theory beyond the local density approximation as an effective tool, complementary to computationally intensive quantum Monte Carlo simulations, for investigating the melting of the supersolid phase and the possible emergence of the hexatic superfluid phase in bosonic systems with various interaction potentials.
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We use quantum Monte Carlo simulations to determine the finite temperature phase diagram and to investigate the thermal and quantum melting of stripe phases in a two-dimensional hard-core boson model. At half filling and low temperatures the stripes melt at a first order transition. In the doped system, the melting transitions of the smectic phase at high temperatures and the superfluid smectic (supersolid) phase at low temperatures are either very weakly first order, or of second order with no clear indications for an intermediate nematic phase.