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arXiv 0902.2225cond-mat.mes-hallcond-mat.str-el
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一维弱连接环中Luttinger液体的持续电流:连续模型的组态相互作用和量子Monte Carlo研究

Persistent current of Luttinger liquid in one-dimensional ring with weak link: Continuous model studied by configuration interaction and quantum Monte Carlo

R. Németh, M. Moško, R. Krčmár, A. Gendiar, M. Indlekofer, L. Mitas

摘要:

本文研究了具有单弱连接的一维连续环中关联无自旋电子的持续流。通过求解多体薛定谔方程,我们计算了几十个电子通过短程对相互作用V(x-x ')相互作用的关联。我们解决了这个多体问题,先进的组态相互作用(CI)和扩散蒙特卡罗(DMC)方法。我们的CI和DMC结果表明,作为环长(L)的函数的持续电流(I)表现出大L的典型的Luttinger液体,$I \propto L^{-1-α}$,其中功率$α$只取决于电子-电子(e-e)相互作用的幂律。对于强电子-电子相互作用,先前的理论预测$α$的公式为$α= {(1 + 2 α_{RG})}^{1/2} - 1$,其中$α_{RG} = [V(0)-V(2k_F)]/2π\hbar v_F$是弱相互作用电子的重整化群结果,V(q)是V(x-x ')的傅里叶变换。我们的数值数据表明,只有当V(x-x ')的范围很小(大致为$d \lesssim 1/2k_F$,更精确地说是$4d^2k_F^2 << 1$)时,这个理论结果才在连续模型中成立。对于强电子-电子相互作用($α_{RG} > 0.25$),我们的CI数据表明,只有10个电子的环已经具有幂律$I \propto L^{-1-α}$,即,10个电子已经足够表现出像Luttinger液体一样的行为。$α_{RG} > 0.25$的DMC数据被所谓的固定相位近似破坏。最后,我们还讨论了Hartree-Fock近似下的e-e相互作用。我们发现,指数衰减的I(L),而不是幂律,然而,对数(I(L))的斜率仍然只取决于参数$α_{RG}$,只要范围V(x -x ')接近零。

英文摘要:

We study the persistent current of correlated spinless electrons in a continuous one-dimensional ring with a single weak link. We include correlations by solving the many-body Schrodinger equation for several tens of electrons interacting via the short-ranged pair interaction V(x - x'). We solve this many-body problem by advanced configuration-interaction (CI) and diffusion Monte Carlo (DMC) methods. Our CI and DMC results show, that the persistent current (I) as a function of the ring length (L) exhibits for large L the power law typical of the Luttinger liquid, $I \propto L^{-1-α}$, where the power $α$ depends only on the electron-electron (e-e) interaction. For strong e-e interaction the previous theories predicted for $α$ the formula $α= {(1 + 2 α_{RG})}^{1/2} - 1$, where $α_{RG} = [V(0)-V(2k_F)]/2π\hbar v_F$ is the renormalisation-group result for weakly interacting electrons, with V(q) being the Fourier transform of V(x-x'). Our numerical data show that this theoretical result holds in the continuous model only if the range of V(x - x') is small (roughly $d \lesssim 1/2k_F$, more precisely $4d^2k_F^2 << 1$). For strong e-e interaction ($α_{RG} > 0.25$) our CI data show the power law $I \propto L^{-1-α}$ already for rings with only ten electrons, i.e., ten electrons are already enough to behave like the Luttinger liquid. The DMC data for $α_{RG} > 0.25$ are damaged by the so-called fixed-phase approximation. Finally, we also treat the e-e interaction in the Hartree-Fock approximation. We find the exponentially decaying I(L) instead of the power law, however, the slope of log(I(L)) still depends solely on the parameter $α_{RG}$ as long as the range of V(x - x') approaches zero.

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