Quantum hydrodynamics for supersolid crystals and quasicrystals

TL;DR

This paper develops a universal analytical framework for supersolid crystals and quasicrystals, extending the Gross-Pitaevskii model to higher orders, enabling phase diagram and vibrational mode predictions that align with numerical and quantum Monte Carlo results.

Contribution

It introduces a higher-order generalization of the Gross-Pitaevskii model for supersolids, facilitating analytical predictions of phase diagrams and vibrational properties.

Findings

Analytical phase diagrams match numerical simulations.

Dispersion relations agree with quantum Monte Carlo results.

Framework applicable to complex anisotropic potentials.

Abstract

Supersolids are theoretically predicted quantum states that break the continuous rotational and translational symmetries of liquids while preserving superfluid transport properties. Over the last decade, much progress has been made in understanding and characterizing supersolid phases through numerical simulations for specific interaction potentials. The formulation of an analytically tractable framework for generic interactions still poses theoretical challenges. By going beyond the usually considered quadratic truncations, we derive a systematic higher-order generalization of the Gross-Pitaevskii mean field model in conceptual similarity with the Swift-Hohenberg theory of pattern formation. We demonstrate the tractability of this broadly applicable approach by determining the ground state phase diagram and the dispersion relations for the supersolid lattice vibrations in terms of the potential parameters. Our analytical predictions agree well with numerical results from direct hydrodynamic simulations and earlier quantum Monte-Carlo studies. The underlying framework is universal and can be extended to anisotropic pair potentials with complex Fourier-space structure.