One-dimensional electron gas interacting with a Heisenberg spin-1/2 chain
One-dimensional electron gas interacting with a Heisenberg spin-1/2 chain
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一维电子气与海森堡自旋 1/2 链相互作用
DOI：
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发表时间：
1999
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通讯作者：
A. Tsvelik
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作者：
O. Zachar;A. Tsvelik
我们分析了一维电子气通过自旋交换相互作用与反铁磁海森堡自旋 1/2 链相互作用的模型。使用特殊极限下的解，我们描述了弱耦合 JK ≪ JH, EF 处自旋间隙固定点的无间隙模式。我们证明，唯一具有发散敏感性的无间隙配对模式是复合奇奇偶校验奇频单线态配对顺序参数，而普通的 BCS 偶奇偶校验单线态配对模式是不相干的。对于 2 腿梯系统，我们注意到可以有一定范围的掺杂，其中化学势仅切割反键合带，而键合带保持半填充。我们认为，在这种状态下，2 腿梯有效地实现了一维近藤-海森堡模型。一维近藤-海森堡模型（K-H 模型）描述了不相称的一维电子气 (1DEG) 通过自旋交换相互作用与海森堡自旋链-1 相互作用。对于KH模型，我们表明唯一具有发散敏感性的无间隙配对模式是复合奇奇偶校验奇频单线态配对顺序参数，而普通BCS偶奇偶校验单线态配对模式是不相干的。此外，我们发现Yamanaka等人的广义Luttinger定理。 [1]，只有引入新的复合电荷密度波（CDW）才能满足。复合 CDW 具有具有“大费米海”特性的幂律相关性，而传统 CDW 相关性呈指数衰减。我们在几个背景下讨论了我们的结果的重要性：首先，我们的分析为一维近藤-海森堡模型的先前处理[2,3]之间的关系提供了新的线索。其次，我们讨论了在 2 腿梯子系统中有效实现 K-H 模型物理的可能性（这种可能性在所有掺杂 2 腿梯子的研究中都被忽略了 [4]）。第三，我们批评了先前关于K-H模型与高温超导体“条纹理论”相关性的建议。我们分析的核心是基于K-H模型的特殊可解极限的推导，以及这种解在重正化群（RG）框架内的含义。先前对 K-H 模型 [2] 的扰动 RG 分析表明，自旋交换相互作用流向某个强耦合固定点，表明形成了具有增强配对相关性的自旋间隙相。对于特定的参数值，我们获得了一个控制良好的解析解，使我们能够枚举和表征所有无间隙模式的量子数。无间隙模式是定点的属性。这意味着流向同一固定点的所有模型都具有相同的无间隙模式。特别是，如果所有弱耦合 K-H 模型都流向一个固定点，那么我们的分析对所有这些模型都有效。 K-H模型（1）由两条不等价的相互作用链组成；一个是一维电子气（由哈密顿量 H 1DEG [5] 描述），另一个是局域自旋 1/2，{~ τ j } 的反铁磁海森堡链。这些链通过自旋交换相互作用相互作用，反铁磁耦合常数 JK > 0。
We analyse a model of a one-dimensional electron gas interacting with an antiferromagnetic Heisenberg spin-1/2 chain via the spin exchange interactions. Using a solution at a special limit, we characterize the gapless modes of the spin gap fixed point at weak coupling JK ≪ JH, EF. we show that the only gapless pairing mode with divergent susceptibility is a composite odd-parity odd-frequency singlet pairing order parameter, while the ordinary BCS even-parity singlet pairing mode is incoherent. For 2-leg ladder systems, we note that it is possible to have a range of doping where the chemical potential cuts only the anti-bonding band while the bonding band remains halffilled. We propose that, in such a state, the 2-leg ladder is effectively realizing the one-dimensional Kondo-Heisenberg model. The one-dimensional Kondo-Heisenberg model (K-H model) describes an incommensurate one-dimensional electron gas (1DEG) interacting with a Heisenberg chain of spins- 1 via spin exchange interaction. For the KH model, we show that the only gapless pairing mode with divergent susceptibility is a composite odd-parity odd-frequency singlet pairing order parameter, while the ordinary BCS even-parity singlet pairing mode is incoherent. In addition, we find that the generalized Luttinger’s theorem of Yamanaka et al. [1], is satisfied only by the introduction of a new composite charge density wave (CDW). The composite CDW has power-law correlations with a ”large-Fermi-sea” characteristics, while conventional CDW correlations decay exponentially. We discuss the significance of our results in several contexts: First, our analysis sheds new light on the relations between previous treatments [2,3] of the one-dimensional Kondo-Heisenberg model. Second, we discuss the possibility of effective realization of K-H model physics in 2-leg ladder systems (This possibility was missed in all previous studies of doped 2-leg ladders [4]). Third, we criticize previous suggestions regarding the relevance of K-H model to ”stripes theories” of high-Tc superconductors. The core of our analysis is based on the derivation of a special solvable limit of the K-H model, and the meaning of such a solution within the renormalization group (RG) framework. The previous perturbative RG analysis of the K-H model [2] has shown that the spin exchange interaction flows to some strong coupling fixed point suggesting the formation of a spin gap phase with enhanced pairing correlations. For particular value of parameters we obtain a well-controlled analytical solution which enables us to enumerate and characterize quantum numbers of all gapless modes. Gapless modes are properties of the fixed point. This means that the same gapless modes characterize all models which flow to the same fixed point. In particular, if there is only one fixed point to which all weak coupling K-H models flow, then our analysis is valid for all of them. The K-H model (1) consists of two inequivalent interacting chains; one is a one-dimensional electron gas (described by the Hamiltonian H 1DEG [5]), and the other an antiferromagnetic Heisenberg chain of localized spins 1/2, {~ τ j }. The chains interact via a spin exchange interaction with an antiferromagnetic coupling constant JK > 0.