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理论物理通讯：英文版

Time-Dependent Evolution of Two Coupled Luttinger Models of Spin-1/2 Fermions

Zhou, Zong-Li, Lou, Ping Ping

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

基于我们考虑由二断开的 Luttinger 液体组成的 spinful 系统的地理论的 bosonization，它在时间 t = 被联合 0 通过 chiral 密度密度相互作用。我们借助于 bosonization 和 Bogoliubov 转变在这个 1D 系统显示出著名纺纱费用分离。评估经分解一个粒子相等时间的关联功能， Cazalilla 的方法被扩大到纺纱费用部门。在关联的行为不与平衡的与一致的长时间限制，二的相等时间的关联联合了 spinful Luttinger 液体，这被发现。以便与试验性的结果作比较，管理非平衡系统的相等时间的关联的幂定律行为的改进代表在这个工作的结束被获得。

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基于我们考虑由二断开的 Luttinger 液体组成的 spinful 系统的地理论的 bosonization，它在时间 t = 被联合 0 通过 chiral 密度密度相互作用。我们借助于 bosonization 和 Bogoliubov 转变在这个 1D 系统显示出著名纺纱费用分离。评估经分解一个粒子相等时间的关联功能， Cazalilla 的方法被扩大到纺纱费用部门。在关联的行为不与平衡的与一致的长时间限制，二的相等时间的关联联合了 spinful Luttinger 液体，这被发现。以便与试验性的结果作比较，管理非平衡系统的相等时间的关联的幂定律行为的改进代表在这个工作的结束被获得。
费米子在相互作用以后被考虑的 spin-1/2 的一个 Luttinger 模型突然在时间 t = 被打开 0。借助于 bosonization 技术，我们评估经分解一个粒子关联详细工作，主要包含相等时间的关联和增殖者。为这个 spinful 非平衡系统管理相等时间的关联的幂定律行为的批评代表被获得。与出版结果比较，在 spinful 和无纺纱的非平衡系统的关联的批评代表之间的差别被发现并且解释。而且，增殖者在这个非平衡系统从另外的相等时间的关联展出不同幂定律行为，这被发现。[从作者抽象]
Based on the field-theoretical bosonization we consider the spinful system consisting of two disconnected Luttinger liquids, which are coupled at time t = 0 through chiral density-density interactions. We show the well-known spin-charge separation in this 1D system by means of bosonization and Bogoliubov transformation. To evaluate analytically the one-particle equal-time correlation functions, Cazalilla's methods are extended to spin-charge sectors. It is found that in long time limit the behavior of correlations does not coincide with that of equilibrium equal-time correlations of two coupled spinful Luttinger liquids. In order to compare with experimental results, the improved exponent that governs the power-law behavior of equal-time correlations of the non-equilibrium system is obtained at the end of this work.
Motivated by recent research achievement of quantum interacting systems in non-equilibrium, we consider a Luttinger model with a suddenly switched-on interaction proposed by Cazalilla [M.A. Cazalilla, Phys. Rev. Lett. 97 (2006) 156403 ]. In order to compare with real systems, we extend Cazalilla's scenario to the spinful system. To find the influence of initial states on the time evolution of some non-equilibrium systems, we mainly focus on the density-density propagator. By comparison and analysis, we discover the different behavior of this non-equilibrium system. Further, it is found that the propagator saves strong memory of initial state, and the effects of right-left interaction cancel out in total density-density propagator.
It is well established that at low energies one-dimensional (1D) fermionic systems are described by the Luttinger-liquid (LL) theory, which predicts phenomena such as spin-charge separation and charge fractionalization into chiral modes. Here we show through the time evolution of an electron injected into a 1D ttt-JJJ model, obtained with time-dependent density matrix renormalization group, that a further fractionalization of both charge and spin takes place beyond the hydrodynamic limit. Its dynamics can be understood at the supersymmetric point (J=2tJ=2tJ=2t) in terms of the excitations of the Bethe-ansatz solution. Furthermore we show that fractionalization with similar characteristics extends to the whole region corresponding to a repulsive LL.