Dimensional interpolation for metallic hydrogen

TL;DR

This paper introduces a dimensional interpolation method to accurately estimate the ground-state energy of metallic hydrogen in three dimensions, analyze phase transitions, and predict physical properties relevant to high-temperature superconductivity.

Contribution

The paper presents a simple dimensional interpolation formula that accurately predicts energies and phase transition properties of metallic hydrogen, extending its applicability to complex many-body systems.

Findings

Accurate estimation of metallic hydrogen's ground-state energy in 3D.

Prediction of phase transition behaviors for different lattice symmetries.

Identification of metallic hydrogen as a candidate for high-temperature superconductivity.

Abstract

We employ a simple and mostly accurate dimensional interpolation formula using dimensional limits $D=1$ and $D=\infty$ to obtain $D=3$ ground-state energy of metallic hydrogen. We also present results describing the phase transitions for different symmetries of three-dimensional structure lattices. The interpolation formula not only predicts fairly accurate energies but also predicts a correct functional form of the energy as a function of the lattice parameters. That allows us to calculate different physical quantities such as the bulk modulus, Debye temperature, and critical transition temperature, from the gradient and the curvature of the energy curve as a function of the lattice parameters. These theoretical calculations suggest that metallic hydrogen is a likely candidate for high temperature superconductivity. The dimensional interpolation formula is robust and might be useful to obtain the energies of complex many-body systems.