Charge carrier relaxation dynamics in the one-dimensional Kondo lattice model

A generic question in the field of ultrafast dynamics is concerned with the relaxation dynamics and the subsequent thermalization of optically excited charge carriers. Among several possible relaxation channels available in a solid-state system, we focus on the coupling to magnetic excitations. In this paper, we study the real-time dynamics of a paradigmatic model, the Kondo lattice model in one dimension. We conduct a comprehensive study of the relaxation processes by evaluating the spin polarization of the conduction electron, the local spin-spin correlation between localized and conduction electrons, and the electronic momentum distribution. While in the well-studied cases of one or two charge carriers in a ferromagnetic background, no thermalization occurs, we demonstrate that the stationary state is compatible with thermalization if either the electronic filling is finite or the magnetic background is in the singlet sector. Our real-time simulations using the time-dependent Lanczos method are corroborated by a direct comparison with finite-temperature expectation values and an analysis of the spectrum in terms of the gap ratio.

💡 Research Summary

This paper presents a comprehensive numerical study of the relaxation and thermalization dynamics of optically excited charge carriers coupled to magnetic excitations, using the one-dimensional Kondo lattice model as a paradigmatic framework. The central question addressed is under what conditions a non-equilibrium initial state evolves towards a thermal equilibrium state.

The model Hamiltonian consists of the kinetic energy of conduction electrons, an on-site exchange (Kondo) coupling J between conduction electron spins and localized spins, an optional antiferromagnetic Heisenberg coupling J_AFM between localized spins, and optional diagonal disorder W for the conduction electrons. The primary observables monitored during the real-time evolution are the spin polarization of the conduction electrons, their momentum distribution function, their kinetic energy, and the local spin-spin correlation between conduction and localized electrons.

The numerical approach relies on the time-dependent Lanczos method for exact time propagation within relevant symmetry sectors (total magnetization, particle number, momentum). Results are corroborated by comparing long-time averages of observables with thermal expectation values calculated via exact diagonalization at a temperature corresponding to the initial state’s energy, and by analyzing the system’s energy level statistics via the gap ratio.

The investigation proceeds through several key scenarios:

1. Single carrier in a ferromagnetic (FM) background: The initial state is a single conduction electron with a defined momentum (k0=π/2) and spin opposite to a fully polarized lattice of localized spins. This case, effectively a few-body problem of an electron and a magnon, shows relaxation but no thermalization. The momentum distribution retains sharp peaks, and the dynamics are integrable. Adding disorder can further suppress thermalization, leading to oscillatory dynamics at strong disorder.
2. Finite density of carriers in an FM background: Increasing the number of conduction electrons (e.g., to a filling of n=1/4) while keeping the FM spin background introduces many-body complexity. Here, the dynamics change qualitatively: the spin polarization decays significantly, and the momentum distribution broadens into a structure centered around k=0. The long-time steady state shows excellent agreement with thermal expectation values, strongly suggesting successful thermalization.
3. Single carrier in a singlet magnetic background: Instead of an FM background, the localized spins are initialized in a correlated antiferromagnetic (singlet) state. Even with just one carrier, the system now resides in a large many-body Hilbert space. The dynamics again exhibit signatures of thermalization: decay of spin polarization, broadening of the momentum distribution, and a thermal-like steady state. The level spacing statistics confirm the non-integrability of this regime.

The main conclusion is that thermalization of a photo-injected charge carrier via coupling to magnetic excitations in the Kondo lattice model is not generic but depends crucially on the initial condition. Thermalization fails in simple, effectively few-body limits like a single carrier in an FM background, which is integrable. However, it becomes robust when the initial state populates a sufficiently large, non-integrable portion of the many-body Hilbert space. This can be achieved either by having a finite density of charge carriers (even in an FM background) or by injecting a carrier into a magnetically correlated (singlet) background. The work thus provides clear criteria for thermalization in this class of models and offers valuable insights for interpreting ultrafast spectroscopy experiments on correlated magnetic materials.