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arXiv:1506.06368 · Physical Review Letters

Quantum Phase Transition and Protected Ideal Transport in a Kondo Chain

Alexei M. Tsvelik, Oleg M. Yevtushenko

Published Nov 16, 2015• 14 citations
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Abstract

We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, Z_{2} symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axis anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localization.

DOI
10.1103/physrevlett.115.216402

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We study the low energy physics of a Kondo chain where electrons from a one-dimensional band interact with magnetic moments via an anisotropic exchange interaction. It is demonstrated that the anisotropy gives rise to two different phases which are separated by a quantum phase transition. In the phase with easy plane anisotropy, Z_{2} symmetry between sectors with different helicity of the electrons is broken. As a result, localization effects are suppressed and the dc transport acquires (partial) symmetry protection. This effect is similar to the protection of the edge transport in time-reversal invariant topological insulators. The phase with easy axis anisotropy corresponds to the Tomonaga-Luttinger liquid with a pronounced spin-charge separation. The slow charge density wave modes have no protection against localization.
We study the low-temperature properties of a one-dimensional spin-1/21/21/2 chain of magnetic impurities coupled to a (normal) metal environment by means of anisotropic Kondo exchange. In the case of easy-plane anisotropy, we obtain the phase diagram of this system at T=0T=0T=0. We show that the in-plane Kondo coupling destabilizes the Tomonaga-Luttinger phase of the spin chain, and leads to two different phases: (i) At strong Kondo coupling, the spins in the chain form Kondo singlets and become screened by the metallic environment, and (ii) at weak and intermediate Kondo coupling, we find a novel dissipative phase characterized by diffusive gapless spin excitations. The two phases are separated by a quantum critical point of the Wilson-Fisher universality class with dynamical exponent $z\ensuremath{\simeq}2$.
We study the Kondo chain in the regime of high spin concentration where the low energy physics is dominated by the Ruderman-Kittel-Kasuya-Yosida interaction.As has been recently shown (Tsvelik and Yevtushenko 2015 Phys.Rev. Lett.115 216402), this model has two phases with drastically different transport properties depending on the anisotropy of the exchange interaction.In particular, the helical symmetry of the fermions is spontaneously broken when the anisotropy is of the easy plane type.This leads to a parametrical suppression of the localization effects.In the present paper we substantially extend the previous theory, in particular, by analyzing a competition of forward-and backward-scattering, including into the theory short range electron interactions and calculating spin correlation functions.We discuss applicability of our theory and possible experiments which could support the theoretical findings.
We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid. Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid. Both phases have full spin gaps and exhibit power-law superconducting pair correlation. The Cooper pair symmetry is singlet dxyd_{xy}dxy​ in the non-trivial phase and triplet Sz=0S_z=0Sz​=0 in the trivial phase. The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary, and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned. As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes. We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.
The effect of a local Kondo coupling and Hubbard interaction on the topological phase of the one-dimensional topological Kondo insulator (TKI) is numerically investigated using the infinite matrix-product state density-matrix renormalization group algorithm. The ground state of the TKI is a symmetry-protected topological (SPT) phase protected by inversion symmetry. It is found that on its own, the Hubbard interaction that tends to force fermions into a one-charge per site order is insufficient to destroy the SPT phase. However, when the local Kondo Hamiltonian term that favors a topologically trivial ground state with a one-charge per site order is introduced, the Hubbard interaction assists in the destruction of the SPT phase. This topological phase transition occurs in the charge sector where the correlation length of the charge excitation diverges while the correlation length of the spin excitation remains finite. The critical exponents, central charge, and the phase diagram separating the SPT phase from the topologically trivial phase are presented.
Topological Kondo insulators are strongly correlated materials where itinerant electrons hybridize with localized spins, giving rise to a topologically nontrivial band structure. Here, we use nonperturbative bosonization and renormalization-group techniques to study theoretically a one-dimensional topological Kondo insulator, described as a Kondo-Heisenberg model, where the Heisenberg spin-1/2 chain is coupled to a Hubbard chain through a Kondo exchange interaction in the p-wave channel (i.e., a strongly correlated version of the prototypical Tamm-Schockley model). We derive and solve renormalization-group equations at two-loop order in the Kondo parameter, and find that, at half filling, the charge degrees of freedom in the Hubbard chain acquire a Mott gap, even in the case of a noninteracting conduction band (Hubbard parameter U=0). Furthermore, at low enough temperatures, the system maps onto a spin-1/2 ladder with local ferromagnetic interactions along the rungs, effectively locking the spin degrees of freedom into a spin-1 chain with frozen charge degrees of freedom. This structure behaves as a spin-1 Haldane chain, a prototypical interacting topological spin model, and features two magnetic spin-1/2 end states for chains with open boundary conditions. Our analysis allows us to derive an insightful connection between topological Kondo insulators in one spatial dimension and the well-known physics of the Haldane chain, showing that the ground state of the former is qualitatively different from the predictions of the naive mean-field theory.
We show that a doped spin-1/2 ladder with antiferromagnetic intra-chain and ferromagnetic inter-chain coupling is a symmetry protected topologically non-trivial Luttinger liquid. Turning on a large easy-plane spin anisotropy drives the system to a topologically-trivial Luttinger liquid. Both phases have full spin gaps and exhibit power-law superconducting pair correlation. The Cooper pair symmetry is singlet dxy in the non-trivial phase and triplet Sz=0 in the trivial phase. The topologically non-trivial Luttinger liquid exhibits gapless spin excitations in the presence of a boundary, and it has no non-interacting or mean-field theory analog even when the fluctuating phase in the charge sector is pinned. As a function of the strength of spin anisotropy there is a topological phase transition upon which the spin gap closes. We speculate these Luttinger liquids are relevant to the superconductivity in metalized integer spin ladders or chains.