Crossover from self-trapped bound states to perturbative scattering in the Heisenberg-Kondo lattice model
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arXiv
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| Natura: | Preprint |
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2025
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| _version_ | 1866915583111462912 |
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| author | Mondal, Tanmoy Majumdar, Pinaki |
| author_facet | Mondal, Tanmoy Majumdar, Pinaki |
| contents | 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 $ρ(T)$ 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 $μ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_24520 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Crossover from self-trapped bound states to perturbative scattering in the Heisenberg-Kondo lattice model Mondal, Tanmoy Majumdar, Pinaki Strongly Correlated Electrons 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 $ρ(T)$ 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 $μ$ 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. |
| title | Crossover from self-trapped bound states to perturbative scattering in the Heisenberg-Kondo lattice model |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2510.24520 |