Electron liquid state in the symmetric Anderson lattice

TL;DR

This paper analytically and numerically investigates the electron liquid state in the symmetric Anderson lattice, revealing a hybridization-induced gap, spontaneous symmetry breaking, and anomalous low-temperature heat capacity behavior.

Contribution

It provides a new analytical and numerical solution for the symmetric Anderson lattice across dimensions, highlighting the electron liquid's properties and spectral gap formation.

Findings

Spectral gap opens due to hybridization at half filling.

Spontaneous symmetry breaking occurs in the electron liquid state.

Anomalous low-temperature heat capacity behavior is observed.

Abstract

Using mean field approach, we provide analytical and numerical solution of the symmetric Anderson lattice for arbitrary dimension at half filling. The symmetric Anderson lattice is equivalent to the Kondo lattice, which makes it possible to study the behavior of an electron liquid in the Kondo lattice. We have shown that, due to hybridization (through an effective field due to localized electrons) of electrons with different spins and momenta $\textbf{k}$ and $\textbf{k}+\overrightarrow{\pi}$, the gap in the electron spectrum opens at half filling. Such hybridization breaks the conservation of the total magnetic momentum of electrons, the spontaneous symmetry is broken. The state of electron liquid is characterized by a large Fermi surface. A gap in the spectrum is calculated depending on the magnitude of the on-site Coulomb repulsion and value of s-d hybridization for the chain, as well as for square and cubic lattices. Anomalous behavior of the heat capacity at low temperatures in the gapped state, which is realized in the symmetric Anderson lattice, was also found.