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Spin-independent v-representability of Wigner crystal oscillations in one-dimensional Hubbard chains: The role of spin-charge separation
Strongly Correlated Electrons · Submitted 22 Jun 2012
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim By means of exact and DMRG solutions, as well as, a new approach of exchange-correlation potential, we show the answer to be positive.
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The abstract, sentence by sentence
Electrons in one-dimension display the unusual property of separating their spin and charge into two independent entities: The first, which derive from uncharged spin-1/2 electrons, can travel at different velocities when compared with the second, built from charged spinless electrons. Predicted theoretically in the early sixties, the 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, the spin-charge separation leads 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 non-magnetized systems, the current density functionals which are applied to the 1D Hubbard model are not seen to reproduce this crossover, referring to a more fundamental question: Are the Wigner crystal oscillations in 1D systems non-interacting v-representable? Or, is there a spin-independent Kohn-Sham potential which is able to yield spin-charge separation? Finding an appropriate answer to both questions is our main task here. By means of exact and DMRG solutions, as well as, a new approach of exchange-correlation potential, 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.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | Electrons in one-dimension display the unusual property of separating their spin and charge into two independent entities: The first, which derive from uncharged spin-1/2 electrons, can travel at different velocities when compared with the second, built from charged spinless electrons. | background 1.00 | 0.04 | 0.02 | asserted 1.00 |
| s1 | Predicted theoretically in the early sixties, the 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. | background 1.00 | 0.03 | 0.02 | asserted 0.57 |
| s2 | In one-dimensional (1D) model systems, the spin-charge separation leads 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. | background 1.00 | 0.06 | 0.04 | asserted 0.96 |
| s3 | In non-magnetized systems, the current density functionals which are applied to the 1D Hubbard model are not seen to reproduce this crossover, referring to a more fundamental question: Are the Wigner crystal oscillations in 1D systems non-interacting v-representable? | gap 0.78 | 0.14 | 0.03 | asserted 0.98 |
| s4 | Or, is there a spin-independent Kohn-Sham potential which is able to yield spin-charge separation? | gap 0.81 | 0.06 | 0.03 | unclear 0.75 |
| s5 | Finding an appropriate answer to both questions is our main task here. | contribution 0.80 | 0.24 | 0.04 | asserted 0.75 |
| s6 | By means of exact and DMRG solutions, as well as, a new approach of exchange-correlation potential, we show the answer to be positive. | result 0.68 | 0.96 | 0.88 | asserted 1.00 |
| s7 | 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. | result 0.60 | 0.91 | 0.65 | asserted 1.00 |
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Original abstract
Electrons in one-dimension display the unusual property of separating their spin and charge into two independent entities: The first, which derive from uncharged spin-1/2 electrons, can travel at different velocities when compared with the second, built from charged spinless electrons. Predicted theoretically in the early sixties, the 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, the spin-charge separation leads 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 non-magnetized systems, the current density functionals which are applied to the 1D Hubbard model are not seen to reproduce this crossover, referring to a more fundamental question: Are the Wigner crystal oscillations in 1D systems non-interacting v-representable? Or, is there a spin-independent Kohn-Sham potential which is able to yield spin-charge separation? Finding an appropriate answer to both questions is our main task here. By means of exact and DMRG solutions, as well as, a new approach of exchange-correlation potential, 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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