[Paper Review] Local magnetic moment formation and Kondo screening in the half filled two dimensional single band Hubbard model

T. B. Mazitov, A. A. Katanin|arXiv (Cornell University)|Nov 24, 2021

Quantum and electron transport phenomena4 citations

TL;DR

This study uses dynamical mean-field theory (DMFT) to analyze local magnetic moment formation and Kondo screening in the half-filled two-dimensional Hubbard model. It identifies distinct temperature regimes via charge and spin susceptibilities, linking a local maximum in charge susceptibility to the onset of local moments and a minimum in both charge susceptibility and double occupancy to full moment formation. The Kondo temperature $T_K$ is extracted using a frequency-resolved fingerprint criterion, showing good agreement with the criterion near the Mott transition but overestimation further away.

ABSTRACT

We study formation of local magnetic moments in strongly correlated Hubbard model within dynamical mean field theory and associate peculiarities of temperature dependence of local charge $χ_c$ and spin $χ_s$ susceptibilities with different stages of local moment formation. Local maximum of temperature dependence of the charge susceptibility $χ_c$ is associated with beginning of local magnetic moments formation, while the minimum of the susceptibility $χ_c$ and double occupation, as well as low temperature boundary of the plateau of effective local magnetic moment $μ_{ m eff}^2=Tχ_s$ temperature dependence are connected with full formation of local moments. We also obtain interaction dependence of the Kondo temperature $T_K$, which is compared to the fingerprint criterion of Phys. Rev. Lett. 126, 056403 (2021). Near the Mott transition the two criteria coincide, while further away from Mott transition the fingerprint criterion somewhat overestimates Kondo temperature. The relation of the observed features to the behavior of eigenvectors/eigenvalues of fermionic frequency-resolved charge susceptibility and divergences of irreducible vertices is discussed.

Motivation & Objective

• To understand the sequence of events in local magnetic moment formation in the strongly correlated half-filled Hubbard model.
• To identify distinct temperature regimes associated with different stages of local moment formation using charge and spin susceptibilities.
• To extract the Kondo temperature $T_K$ using a frequency-resolved criterion and assess its validity near the Mott metal-insulator transition.
• To relate the observed features to the eigenvectors and eigenvalues of the fermionic frequency-resolved charge susceptibility and to divergences in irreducible vertices.

Proposed method

• Employing dynamical mean-field theory (DMFT) to solve the single-band Hubbard model on a two-dimensional square lattice.
• Calculating local charge susceptibility $\chi_c$ and spin susceptibility $\chi_s$ as functions of temperature and interaction strength $U$.
• Using the frequency-resolved 'fingerprint criterion' $\chi_c^{\nu_1\nu_1} = \chi_c^{\nu_1,-\nu_1}$ at Matsubara frequencies $\nu_1 = \pm \pi T$ to identify $T_K$.
• Analyzing the eigenvectors and eigenvalues of the $2 \times 2$ fermionic frequency subspace of the charge susceptibility to interpret the physical origin of the observed features.
• Comparing the extracted $T_K$ with the Kondo temperature from the Kondo model and assessing consistency with the fingerprint criterion.
• Investigating the spectral function and quasi-particle peak width via numerical renormalization group (NRG) to validate the temperature scales.

Experimental results

Research questions

• RQ1 At what temperature does local magnetic moment formation begin, and how is it signaled in the charge susceptibility?
• RQ2 What temperature marks the full formation of local magnetic moments, and how is this reflected in $\chi_c$, double occupancy, and $\mu_{\text{eff}}^2$?
• RQ3 How does the Kondo temperature $T_K$ extracted from the fingerprint criterion compare to the actual Kondo screening scale near the Mott transition?
• RQ4 What is the role of the eigenvectors and eigenvalues of the frequency-resolved charge susceptibility in characterizing moment formation and screening?
• RQ5 How do the divergences in irreducible vertices and the behavior of the spectral function relate to the observed features in the susceptibilities?

Key findings

• The local maximum in the temperature dependence of the charge susceptibility $\chi_c$ signals the onset of local magnetic moment formation.
• The minimum in $\chi_c$ and double occupancy, along with the low-temperature plateau in $\mu_{\text{eff}}^2 = T\chi_s$, mark the full formation of local magnetic moments.
• The Kondo temperature $T_K$ extracted via the fingerprint criterion agrees well with the Kondo model prediction near the Mott transition.
• Further from the Mott transition, the fingerprint criterion slightly overestimates $T_K$, indicating a breakdown in its universal applicability.
• The quasi-particle peak width $\nu_{\text{QP}}$ is approximately $5T_{c,\text{min}}$, where $T_{c,\text{min}}$ is the temperature at which moments are fully formed.
• The spectral function and local spin susceptibility remain approximately constant in units of $T_K$ at low temperatures, confirming the consistency of the $T_K$ determination.