Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier.Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction.The persistent current is a sine-like function of magnetic flux.It decays with the ring length (L) faster than L -1 and eventually like L -α-1 , where α > 0 is universal.Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier.Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction.The persistent current is a sine-like function of magnetic flux.It decays with the ring length (L) faster than L -1 and eventually like L -α-1 , where α > 0 is universal.

Acta Physica Polonica ANov 1, 20051 citation

Interacting electrons in one dimension: Luttinger liquids

Heinz J. Schulz

Physica C SuperconductivityDec 1, 19944 citations

Interaction electrons in one dimension : The Luttinger liquid

Rampadarath Anand, Sach Mulchan

Mar 13, 20120 citations

Spinless Hartree-Fock model of persistent current in rings with single scatterer: Comparison with correlated models

Radoslav Németh, Martin Moško

Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study the persistent current of the interacting electron gas in a one-dimensional continuous ring containing a single $δ$ barrier. We calculate the persistent current as a function of the ring circumference, magnetic flux threading the ring, barrier strength, etc. We compare our results with the results of correlated models like the Luttinger liquid model and the Hubbard model solved by means of the renormalization group. A good agreement is found. First, the persistent current decays with the increasing ring circumference ( $L$ ) faster than $L^{-1}$ and eventually like $L^{-α-1}$ , where $α>0$ depends only on the electron-electron interaction. Second, the persistent current is a sine-shaped function of magnetic flux. This sine-like dependence and in particular the universal power law $L^{-α-1}$ have sofar been believed to arise only in the correlated many-body models. Observation of these features within the Hartree-Fock model is a surprising result.Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study the persistent current of the interacting electron gas in a one-dimensional continuous ring containing a single $δ$ barrier. We calculate the persistent current as a function of the ring circumference, magnetic flux threading the ring, barrier strength, etc. We compare our results with the results of correlated models like the Luttinger liquid model and the Hubbard model solved by means of the renormalization group. A good agreement is found. First, the persistent current decays with the increasing ring circumference ($L$) faster than $L^{-1}$ and eventually like $L^{-α-1}$, where $α>0$ depends only on the electron-electron interaction. Second, the persistent current is a sine-shaped function of magnetic flux. This sine-like dependence and in particular the universal power law $L^{-α-1}$ have sofar been believed to arise only in the correlated many-body models. Observation of these features within the Hartree-Fock model is a surprising result.

arXiv:cond-mat/0503146Mar 7, 20050 citations

Tunneling in one-dimensional non-Luttinger electron liquid

К. А. Матвеев, Dongxiao Yue, L. I. Glazman

The conductance of a weakly interacting electron gas in the presence of a single scatterer is found at arbitrary strength of the scattering potential. At weak interaction, a simple renormalization group approach can be used instead of the standard bosonization procedure. Our technique allows us to take into account the backscattering of electrons that leads to deviations of the low-temperature conductance from the behavior typical for Luttinger liquid. In the presence of magnetic field, the backscattering may give rise to a peak in differential conductance at bias equal to the Zeeman energy.The conductance of a weakly interacting electron gas in the presence of a single scatterer is found at arbitrary strength of the scattering potential. At weak interaction, a simple renormalization group approach can be used instead of the standard bosonization procedure. Our technique allows us to take into account the backscattering of electrons that leads to deviations of the low-temperature conductance from the behavior typical for Luttinger liquid. In the presence of magnetic field, the backscattering may give rise to a peak in differential conductance at bias equal to the Zeeman energy.

arXiv:cond-mat/9306041Physical Review LettersNov 15, 1993219 citations

δ

barrier. We calculate the persistent current as a function of the ring circumference, magnetic flux threading the ring, barrier strength, etc. We compare our results with the results of correlated models like the Luttinger liquid model and the Hubbard model solved by means of the renormalization group. A good agreement is found. First, the persistent current decays with the increasing ring circumference (

L

) faster than

L^{-1}

and eventually like

L^{-α-1}

, where

α>0

depends only on the electron-electron interaction. Second, the persistent current is a sine-shaped function of magnetic flux. This sine-like dependence and in particular the universal power law

L^{-α-1}

have sofar been believed to arise only in the correlated many-body models. Observation of these features within the Hartree-Fock model is a surprising result.