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arXiv:1304.5256 · Physical Review B

Inhomogeneous superconducting phases in the frustrated Kondo-Heisenberg chain

A. Dobry, Akbar Jaefari, Eduardo Fradkin

Published Jun 7, 2013• 8 citations
arXivHTMLPDF

Abstract

We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-$\frac{1}{2}$ Luttinger liquid coupled by a Kondo exchange interaction ${J}_{K}$ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling ${J}_{1}$ and a next-nearest-neighbor (frustrating) exchange interaction ${J}_{2}$. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling ${J}_{K}$ with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios ${J}_{K}/{J}_{1}$, ${J}_{2}/{J}_{1}$, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.

DOI
10.1103/physrevb.87.245102

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We use bosonization and renormalization group methods to determine the ground-state phase diagram of a one-dimensional frustrated Kondo-Heisenberg system consisting of a one-dimensional spin-12\frac{1}{2}21​ Luttinger liquid coupled by a Kondo exchange interaction JK{J}_{K}JK​ to a frustrated quantum antiferromagnetic Heisenberg chain, with a nearest-neighbor exchange coupling J1{J}_{1}J1​ and a next-nearest-neighbor (frustrating) exchange interaction J2{J}_{2}J2​. We analyze the interplay of quantum frustration in the antiferromagnetic chain with the Kondo exchange coupling JK{J}_{K}JK​ with the Luttinger liquid. We discuss the structure of the phase diagram of this system as a function of the ratios JK/J1{J}_{K}/{J}_{1}JK​/J1​, J2/J1{J}_{2}/{J}_{1}J2​/J1​, and of the parameters of the Luttinger liquid. In particular, we discuss in detail the regimes in which a pair-density-wave state may be realized and its relation with the spin correlations in the frustrated antiferromagnetic chain.
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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.
We investigate the Hubbard chain at half band filling with additional nearest-neighbor and next-nearest-neighbor spin exchange J1{J}_{1}J1​ and J2{J}_{2}J2​ using bosonization and the density-matrix renormalization group. For J2=0{J}_{2}=0J2​=0 we find a spin-density-wave phase for all positive values of the Hubbard interaction UUU and the Heisenberg exchange J1{J}_{1}J1​. A frustrating spin exchange J2{J}_{2}J2​ induces a bond-order-wave phase. For some values of J1{J}_{1}J1​, J2{J}_{2}J2​, and UUU, we observe a spin-gapped metallic Luther-Emery phase.
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