[论文解读] Probing frustrated spin systems with impurities

Maksymilian Kliczkowski, Jakub Grabowski+1 more|arXiv (Cornell University)|Feb 24, 2026

Advanced Condensed Matter Physics被引用 0

一句话总结

本文分析嵌入在受挫的 J1–J2 Heisenberg 链中的两个经典自旋杂质之间的有效相互作用，在弱耦合下呈现 RKKY 式行为，强耦合时呈现由奇偶性支配、边界驱动的效应，并在整个相图上给出 DMRG 结果。

ABSTRACT

We investigate the effective interaction between two localized spin impurities embedded in a frustrated spin-1/2 $J_1\!-\!J_2$ Heisenberg chain. Treating the impurity spins as classical moments coupled locally to the host, we combine second--order perturbation theory with large--scale density matrix renormalization group (DMRG) calculations to determine the impurity--impurity interaction as a function of separation, coupling strength, and magnetic frustration. In the weak--coupling regime, we show that the interaction is governed by the the static spin susceptibility of the host and exhibits oscillatory power--law decay in the gapless phase, modified by universal logarithmic corrections at the SU(2)--symmetric critical point. In the gapped dimerized phase, the interaction decays exponentially with distance. For intermediate and strong impurity--host coupling, we observe a crossover to a boundary--dominated regime characterized by pronounced parity effects associated with the length of the chain segment between impurities, signaling a breakdown of the simple RKKY--like description. Our results establish impurity--impurity interactions as a sensitive probe of frustrated quantum spin liquids and provide a controlled framework for distinguishing gapless and gapped phases through local perturbations.

研究动机与目标

• 研究两局域化杂质如何通过受挫的自旋-1/2 J1–J2 链耦合。
• 确定杂质-杂质相互作用随分离、耦合强度与挫折的函数关系。
• 将相互作用与宿主链的静态自旋易感性及相（无缝隙/有隙）联系起来。
• 评估在不同耦合区间对简单的 RKKY 式描述的失效。

提出的方法

• 将杂质自旋视为局部耦合到宿主链的经典矩。
• 在弱耦合区域使用二阶微扰推导有效相互作用。
• 将横向项能量与宿主链的延迟自旋易感性（χ_ab）相关联。
• 使用 DMRG 计算基态能量并在各个区间提取 V(r,θ)。
• 分析对称性约束，证明在 SU(2) 不变性下杂质能量取决于 S_c1·S_c2。

Figure 1: Illustration how the chain is divided into three segments for $J_{c}\to\infty$ .

实验结果

研究问题

• RQ1 在 gapless（朗缇共振液）与 gapped（二聚化）相中，杂质-杂质相互作用随距离的衰减如何不同？
• RQ2 在临界点上，SU(2) 对称性与边际算子对衰减形式有何作用？
• RQ3 当 J_c 增大时，相互作用如何从体相（RKKY 风格）转变为边界主导的描述？

主要发现

• 在弱耦合区域，V(r) ∝ Re χ(r,0)，在 gapless 相中呈现振荡的幂律衰减。
• 在 SU(2) 对称的临界点，衰减获得普适的对数校正。
• 在带隙二聚化相中，相互作用随距离呈指数衰减，形式为 ∝ e^{-r/ξ}。
• 对中间/强耦合，来自两杂质之间分段长度的奇偶效应主导，标志着对 RKKY 描述的崩溃。
• DMRG 结果支持微扰预测，并揭示从体介导到边界主导的杂质相互作用的转变。

Figure 2: Illustration how the components of the interaction energy ( 14 ) is calculated.