Friedel oscillations in one-dimensional metals: From Luttinger's theorem to the Luttinger liquid

Vieira, Daniel; Freire, Henrique J. P.; Campo, Vivaldo L.; Capelle, K.

doi:10.1016/j.jmmm.2008.02.077

Cited by 15 publications

(26 citation statements)

References 9 publications

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“…4(a), while BALDA/FN yields the correct behavior for weak interaction, the 2k F → 4k F crossover is not recovered as U is increased, following the same trends already observed in the literature. [19][20][21] The same occurs with the BALDA/FN XC potentials of Fig. 4(b), which oscillate in 2k F for all values of U (identified by the eight negative peaks).…”

Section: B Approximated Exchange-correlation Potentialssupporting

confidence: 67%

Spin-independent V-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation

Vieira

2012

Phys. Rev. B

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Electrons in one dimension display the unusual property of separating their spin and charge into two independent entities: The first, which derives from uncharged spin-1/2 electrons, can travel at different velocities when compared with the second, which is built from charged spinless electrons. Predicted theoretically in the early 1960s, spin-charge separation has attracted renewed attention since the first evidences of experimental observation, with usual mentions as a possible explanation for high-temperature superconductivity. In one-dimensional (1D) model systems, spin-charge separation causes the frequencies of Friedel oscillations to suffer a 2k F → 4k F crossover, mainly when dealing with strong correlations, where they are referred to as Wigner crystal oscillations. In nonmagnetized systems, the current density functionals that are applied to the 1D Hubbard model are not seen to reproduce this crossover, which leads to a more fundamental question: Are the Wigner crystal oscillations in 1D systems noninteracting V-representable? Or, is there a spin-independent Kohn-Sham potential that is able to yield spin-charge separation? Finding an appropriate answer to both questions is our main task here. By means of exact and density matrix renormalization group solutions, as well as an exchange-correlation potential introduced here, we show the answer to be positive. Specifically, the V-representable 4k F oscillations emerge from attractive interactions mediated by positively charged spinless holes-the holons-as an additional contribution to the repulsive on-site Hubbard interaction.

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Section: B Approximated Exchange-correlation Potentialssupporting

confidence: 67%

Spin-independent V-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation

Vieira

2012

Phys. Rev. B

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“…However, for such interaction strengths, the shortcomings of the Bethe ansatz LDA can become particularly severe. 126 Nevertheless, it is quite interesting that a competing regime between disorder and interactions is accounted for within our lattice DFT-LDA approach, and with disorder occurring only in a subregion of the system.…”

Section: In Equilibrium: the Inverse Participation Ratiomentioning

confidence: 99%

Interacting fermions in one-dimensional disordered lattices: Exploring localization and transport properties with lattice density-functional theories

et al. 2013

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We investigate the static and dynamical behavior of one-dimensional interacting fermions in disordered Hubbard chains contacted to semi-infinite leads. The chains are described via the repulsive Anderson-Hubbard Hamiltonian, using static and time-dependent lattice density-functional theory. The dynamical behavior of our quantum transport system is studied using an integration scheme available in the literature, which we modify via the recursive Lanczos method to increase its efficiency. To quantify the degree of localization due to disorder and interactions, we adapt the definition of the inverse participation ratio to obtain an indicator which is suitable for quantum transport geometries and can be obtained within density-functional theory. Lattice density-functional theories are reviewed and, for contacted chains, we analyze the merits and limits of the coherent-potential approximation in describing the spectral properties, with interactions included via lattice density-functional theory. Our approach appears to be able to capture complex features due to the competition between disorder and interactions. Specifically, we find a dynamical enhancement of delocalization in the presence of a finite bias and an increase of the steady-state current induced by interparticle interactions. This behavior is corroborated by results for the time-dependent densities and for the inverse participation ratio. Using short isolated chains with interaction and disorder, a brief comparative analysis between time-dependent density-functional theory and exact results is then given, followed by general concluding remarks.

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“…The Hubbard systems studied in Ref. [23][24][25][26] correspond to the case with V = 0, for which no sharp peaks emerge. Next we consider the Hubbard model with long-range dipole-dipole interactions described by the Hamiltonian of Eq.5 with α = 3.…”

Section: B Hubbard Model With Long-range Interactionmentioning

confidence: 99%

Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions

Xu¹,

Li²,

Xianlong³

et al. 2012

J. Phys.: Condens. Matter

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The ground state properties of Hubbard model with or without long-range interactions in the regime with strongly repulsive on-site interaction are investigated by means of the exact diagonalization method. We show that the appearance of N -crests in the density profile of a trapped N-fermion system is a natural result of "fermionization" between antiparallel-spin fermions in the strongly repulsive limit and can not be taken as the only signature of Wigner crystal phase, as the static structure factor does not show any signature of crystallization. On the contrary, both the density distribution and static structure factor of Hubbard model with strong long-range interactions display clear signature of Wigner crystal. Our results indicate the important role of long-range interaction in the formation of Wigner crystal.

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Friedel oscillations in one-dimensional metals: From Luttinger's theorem to the Luttinger liquid

Cited by 15 publications

References 9 publications

Spin-independent V-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation

Spin-independent V-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation

Interacting fermions in one-dimensional disordered lattices: Exploring localization and transport properties with lattice density-functional theories

Wigner crystal versus fermionization for one-dimensional Hubbard models with and without long-range interactions

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