Low-energy excitations and transport functions of the one-dimensional Kondo insulator

TL;DR

This study uses advanced numerical methods to explore the low-temperature excitations and transport properties of a one-dimensional Kondo insulator, revealing distinct behaviors of charge and spin correlations and conductivities.

Contribution

It provides a detailed analysis of low-energy excitations and transport functions in a 1D Kondo insulator using variational matrix product states, highlighting differences in charge and spin dynamics.

Findings

Low-lying spin excitations emerge near the Kondo temperature.

Charge correlations vanish at high temperatures, unlike spin correlations.

Charge and thermal conductivities are affected differently by two-particle correlations.

Abstract

Using variational matrix product states, we analyze the finite temperature behavior of a half-filled periodic Anderson model in one dimension, a prototypical model of a Kondo insulator. We present an extensive analysis of single-particle Green's functions, two-particle Green's functions, and transport functions creating a broad picture of the low-temperature properties. We confirm the existence of energetically low-lying spin excitations in this model and study their energy-momentum dispersion and temperature dependence. We demonstrate that charge-charge correlations at the Fermi energy exhibit a different temperature dependence than spin-spin correlations. While energetically low-lying spin excitations emerge approximately at the Kondo temperature, which exponentially depends on the interaction strength, charge correlations vanish already at high temperatures. Furthermore, we analyze the charge and thermal conductivity at finite temperatures by calculating the time-dependent current-current correlation functions. While both charge and thermal conductivity can be fitted for all interaction strengths by gapped systems with a renormalized band gap, the gap in the system describing the thermal conductivity is generally smaller than the system describing the charge conductivity. Thus, two-particle correlations affect the charge and heat conductivities in a different way resulting in a temperature region where the charge conductivity of this one-dimensional Kondo insulator is already decreasing while the heat conductivity is still increasing.