Crossover from self-trapped bound states to perturbative scattering in the Heisenberg-Kondo lattice model

TL;DR

This paper maps the transport phase diagram of the 2D Heisenberg-Kondo lattice model, revealing a crossover from perturbative scattering to polaronic bound states at low density and strong coupling, with implications for resistivity behavior.

Contribution

It provides a comprehensive analysis of the transport phases in the 2D Heisenberg-Kondo lattice, identifying the conditions for polaron formation and characterizing the resistivity in different regimes.

Findings

Homogeneous electron systems show monotonic resistivity increase with temperature.

At low density and strong coupling, electrons form polarons, causing non-monotonic resistivity peaks.

A universal resistivity form is established in the scattering regime.

Abstract

We map out the complete transport phase diagram of the ferromagnetic Heisenberg-Kondo lattice model in two dimensions. The model involves tight-binding electrons with hopping $t$, coupled to classical spins with coupling $J'$, while the spins have a nearest neighbour coupling $J$ between them. We work with a fixed, small $J/t$, and study the temperature dependence of resistivity for varying electron density $n$ and coupling $J'/t$. Our magnetic configurations are generated by exact diagonalisation-based Langevin dynamics, while the conductivity is computed using the Kubo formula on exact eigenstates. We work on lattices of size $20 \times 20$ and can access electron density down to $n \sim 0.01$. The electron system remains homogeneous either when the mean density is large or when the coupling $J'$ is small. In these situations, the resistivity $\rho(T)$ displays a monotonic increase with temperature and can be understood within a perturbative framework. However, at very low density $n \lesssim 0.05$, strong coupling $J'/t \gtrsim 1$, and for $T \sim T_c$, the electrons can locally polarise the magnetic state, create a trapping potential, and form a bound state in it. The resistivity associated with this polaronic phase is distinctly non-monotonic, with a peak near $T_c$. We establish the boundary that separates the many-body polaronic window from traditional scattering and extract a universal form for the resistivity in the scattering regime. We suggest the origin of the `excess resistivity' in the polaronic regime in terms of an increasing fraction of localised states as the temperature tends to $T_c$. This pushes the mobility edge towards the chemical potential $\mu$ and results in enhanced scattering of momentum states near $k_F$. While our specific results are in two dimensions, the phenomenology we uncover should be valid even in three dimensions.