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arXiv:2203.07367 · Physical Review Letters

Algebraic Hastatic Order in One-Dimensional Two-Channel Kondo Lattice

Milan Kornjača, Rebecca Flint

Published Jul 11, 2024• 3 citations
arXivHTMLPDF

Abstract

The two-channel Kondo lattice likely hosts a rich array of phases, including hastatic order, a channel symmetry breaking heavy Fermi liquid. We revisit its one-dimensional phase diagram using density matrix renormalization group and, in contrast to previous work, find algebraic hastatic orders generically for stronger couplings. These are heavy Tomonaga-Luttinger liquids with nonanalyticities at Fermi vectors captured by hastatic density waves. We also find a predicted additional nonlocal order parameter due to interference between hastatic spinors, not present at large N, and residual repulsive interactions at strong coupling suggesting non-Fermi-liquid physics in higher dimensions.

DOI
10.1103/physrevlett.133.026503

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The two-channel Kondo lattice likely hosts a rich array of phases, including hastatic order, a channel symmetry breaking heavy Fermi liquid. We revisit its one-dimensional phase diagram using density matrix renormalization group and, in contrast to previous work, find algebraic hastatic orders generically for stronger couplings. These are heavy Tomonaga-Luttinger liquids with nonanalyticities at Fermi vectors captured by hastatic density waves. We also find a predicted additional nonlocal order parameter due to interference between hastatic spinors, not present at large N, and residual repulsive interactions at strong coupling suggesting non-Fermi-liquid physics in higher dimensions.
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Recent developments in the theoretical investigation of the one-dimensional Kondo lattice model by using the density matrix renormalization group (DMRG) method are discussed in this review. Short summaries are given of the zero-temperature DMRG method, the finite-temperature DMRG method, and also the application of the finite- T DMRG to dynamic quantities. Away from half-filling, the paramagnetic metallic state is shown to be a Tomonaga-Luttinger liquid with a large Fermi surface. The size of the large Fermi surface is determined by the sum of the densities of the conduction electrons and the localized spins. The correlation exponent of this metallic phase is smaller than 1/2. At half-filling the ground state is insulating. The excitation gaps are different, depending on the channels, the spin gap, the charge gap and the quasiparticle gap. The temperature dependence of the spin and charge susceptibilities and the specific heat are discussed. Particularly interesting is the temperature dependence of various excitation spectra, which indicates unusual properties for the Kondo insulators.
The quantum phase transition from a spin-Peierls phase with a small Fermi surface to a paramagnetic Luttinger-liquid phase with a large Fermi surface is studied in the framework of a one-dimensional Kondo-Heisenberg model that consists of an electron gas away from half filling, coupled to a spin-1/2 chain by Kondo interactions. The Kondo spins are further coupled to each other with isotropic nearest-neighbor and next-nearest-neighbor antiferromagnetic Heisenberg interactions which are tuned to the Majumdar-Ghosh point. Focusing on three-eighths filling and using the density-matrix renormalization-group (DMRG) method, we show that the zero-temperature transition between the phases with small and large Fermi momenta appears continuous, and involves a new intermediate phase where the Fermi surface is not well defined. The intermediate phase is spin gapped and has Kondo-spin correlations that show incommensurate modulations. Our results appear incompatible with the local picture for the quantum phase transition in heavy fermion compounds, which predicts an abrupt change in the size of the Fermi momentum.