Quantum phase transitions in one-dimensional nanostructures: a comparison between DFT and DMRG methodologies

Area of Science:

• Quantum Chemistry
• Computational Materials Science
• Condensed Matter Physics

Background:

• Accurate prediction of electronic structure in nanostructures is a significant challenge in quantum chemistry.
• Density functional theory (DFT) and density matrix renormalization group (DMRG) are key computational methods for electronic correlation.
• Comparing DFT and DMRG provides insights into their performance for diverse molecular systems.

Purpose of the Study:

• To comparatively analyze ground-state energies, density profiles, and entanglement entropies using DFT and DMRG.
• To evaluate the performance of DFT and DMRG for homogeneous, superlattice, and confined nanostructures.
• To identify the strengths and limitations of each method across different electronic phases (metal, insulator, metal-insulator transition).

Main Methods:

• Density functional theory (DFT) calculations using the Kohn-Sham scheme and BALDA approach.
• Integration of the numerical Bethe-Ansatz (BA) solution for homogeneous density functional within LDA.
• Density matrix renormalization group (DMRG) implemented with ITensor library based on matrix product states (MPS) ansatz.

Main Results:

• For homogeneous systems, DFT deviations decrease with chain size, with a clear hierarchy.
• For superlattices, DFT precision decreases with increased impurity numbers in the unit cell.
• DFT performs better for metallic phases in confined chains; higher deviations are observed for Mott and band-insulator phases.

Conclusions:

• The relative accuracy of DFT and DMRG depends significantly on the nanostructure's complexity and electronic phase.
• DFT exhibits limitations in accurately describing superlattices and confined insulating systems.
• DMRG provides a more reliable approach for complex nanostructure electronic property predictions where DFT struggles.