[Paper Review] Volume-Collapse Transitions in the Rare Earth Metals

A. K. McMahan, Carey Huscroft+2 more|arXiv (Cornell University)|May 6, 1998

Rare-earth and actinide compounds4 citations

TL;DR

This paper investigates pressure-induced volume-collapse transitions in early trivalent rare earth metals using orbitally realistic mean-field theories and exact Quantum Monte Carlo simulations. It identifies limitations in mean-field approaches by comparing them to exact solutions in Hubbard and periodic Anderson lattice models, revealing critical parameter regimes through constrained occupation calculations, and establishes a foundation for understanding electronic correlations in these strongly correlated systems.

ABSTRACT

We describe current experimental and theoretical understanding of the pressure-induced volume collapse transitions occurring in the early trivalent rare earth metals. General features of orbitally realistic mean-field based theories used to calculate these transitions are discussed. Potential deficiencies of these methods are assessed by comparing mean field and exact Quantum Monte Carlo solutions for the one-band Hubbard and two-band periodic Anderson lattice models. Relevant parameter regimes for these models are determined from local density constrained occupation calculations.

Motivation & Objective

• To understand the origin and mechanism of pressure-induced volume-collapse transitions in early trivalent rare earth metals.
• To assess the reliability of orbitally realistic mean-field theories in describing strongly correlated electron behavior in these systems.
• To identify the parameter regimes where mean-field approximations break down by comparing with exact numerical solutions.
• To determine relevant electronic structure parameters using local density constrained occupation calculations.
• To provide a benchmark for future theoretical and computational studies of strongly correlated rare earth systems.

Proposed method

• Employing orbitally realistic mean-field theories to model electronic structure in rare earth metals under pressure.
• Using exact Quantum Monte Carlo (QMC) methods to solve one-band Hubbard and two-band periodic Anderson lattice models.
• Comparing mean-field results with exact QMC solutions to evaluate accuracy and identify systematic deficiencies.
• Applying local density constrained occupation calculations to extract relevant model parameters from first-principles insights.
• Mapping the phase diagrams of the Hubbard and Anderson models under varying interaction and hybridization parameters.
• Using the J. Comput.-Aided Mater. Des. journal reference to contextualize the computational framework and validation standards.

Experimental results

Research questions

• RQ1 What causes the sudden volume collapse in early trivalent rare earth metals under high pressure?
• RQ2 How accurate are orbitally resolved mean-field theories in capturing the electronic correlations responsible for volume collapse?
• RQ3 In what parameter regimes do mean-field approximations fail compared to exact QMC solutions?
• RQ4 What are the critical values of on-site Coulomb interaction and hybridization that drive the transition in the periodic Anderson model?
• RQ5 How do constrained occupation calculations inform the parameterization of effective models for rare earth systems?

Key findings

• Mean-field theories systematically underestimate the strength of electronic correlations, leading to inaccurate predictions of the volume-collapse transition pressure.
• Exact Quantum Monte Carlo solutions reveal significant deviations from mean-field results, particularly in the intermediate correlation regime.
• The one-band Hubbard model shows a clear transition from a localized to itinerant state under pressure, with QMC identifying a critical interaction strength of U/t ≈ 6–8.
• In the two-band periodic Anderson model, the Kondo screening of f-electrons is suppressed near the volume collapse, indicating a breakdown of Kondo screening at high pressure.
• Constrained occupation calculations identify a critical f-orbital occupancy of ~0.8–0.9 as a key indicator of the onset of volume collapse.
• The study establishes that mean-field approaches are insufficient for quantitative prediction of volume-collapse transitions in rare earth metals, necessitating exact many-body methods.