Intricately Entangled Spin and Charge Diffusion and the Coherence-Incoherence Crossover in the High-Dimensional Hubbard Model

TL;DR

This study uses advanced numerical methods to analyze spin and charge diffusion in the Hubbard model, revealing how these excitations evolve with temperature and doping, and elucidating the microscopic mechanisms behind coherence-incoherence crossovers.

Contribution

It provides a detailed comparison of NRG methods in capturing low-frequency spectral features and offers new insights into the microscopic origins of coherence-incoherence crossovers in correlated electron systems.

Findings

Spin and charge fluctuations crossover at different temperatures.

Identification of characteristic frequency scales for excitations.

Explanation of two-stage Fermi-to-bad metal transition.

Abstract

Correlation-driven metal-insulator transitions and temperature-driven quantum-coherent-to-incoherent crossovers in correlated electron systems underpin the doping, temperature and frequency-resolved evolution of physical responses. Motivated by recent experimental studies that investigate the evolution of dynamical spin and charge responses, we analyze the spin and charge diffusion spectra in both half-filled and doped one-band Hubbard model using Dynamical Mean Field Theory (DMFT) combined with the Numerical Renormalization Group (NRG). We compare the relative strengths and limitations of Density Matrix NRG (DMNRG) and Full Density Matrix NRG (FDM-NRG) in capturing low-frequency spectral features and their evolution with temperature, interaction strength and band-filling. Key measures, including characteristic frequency scales, Kullback-Leibler divergence, diffusion constants, and kurtosis provide complementary but internally consistent picture for the evolution of spin and charge excitations across bandwidth as well as the band-filling driven Mott transitions and the coherent-incoherent crossover. We find that spin and charge fluctuations cross over from quantum-coherent-to-quantum-incoherent at distinct temperatures, providing a microscopic insight into the complex, two-stage, Fermi-to-non-Fermi liquid-to-bad metal crossovers seen in transport data, in particular in the $dc$ resistivity.