AI 中文总结
研究含铜离子三种价态的自旋-赝自旋X锯齿链，用转移矩阵法分析其自由能等，揭示基态有反铁磁相及三个受挫相，有限温度下零温相界演变成赝转变，展现锯齿几何结构对受挫和短程相干及赝转变行为的促进作用。
AI 中文摘要
我们对一个包含铜离子三种不同价态的自旋-赝自旋X锯齿链进行了精确分析，该链作为由角共享铜三角形组成的一维铜酸盐的最小模型。该模型包括沿基位点以及基位点与顶点位点之间的磁交换和静电耦合常数，捕捉了自旋和电荷自由度之间的竞争。使用转移矩阵方法，我们推导出自由能的精确表达式，并获得定义与明显热力学异常相关的赝临界线的解析条件。基态分析揭示了除反铁磁相之外的三个受挫相，其具有不同的剩余熵。在有限温度下，这些零温度相边界演变成窄熵脊，标志着相应准相之间的赝转变。比热和避免交叉尺度在赝临界温度处表现出尖锐但连续的峰值，而物理相关长度可能由不同的次主导本征值控制。局部相关函数揭示了从电荷主导到磁相关区域的协同重排。我们的结果表明，锯齿几何结构促进了受挫和短程相干，导致明显的赝转变行为。
英文摘要
We present an exact analysis of a spin--pseudospin X sawtooth chain that incorporates three distinct valence states of copper ions and serves as a minimal model for one-dimensional cuprates composed of corner-sharing copper triangles. The model includes magnetic exchange and electrostatic coupling constants both along the base sites and between base and apex sites capturing the competition between spin and charge degrees of freedom. Using the transfer-matrix method, we derive exact expressions for the free energy and obtain an analytical condition defining the pseudo-critical line associated with pronounced thermodynamic anomalies. The ground-state analysis reveals, besides an antiferromagnetic phase, three frustrated phases characterized by distinct residual entropies. At finite temperatures, these zero-temperature phase boundaries evolve into narrow entropy ridges signaling pseudo-transitions between the corresponding quasi-phases. The specific heat and the avoided-crossing scale exhibit sharp but continuous peaks at the pseudo-critical temperature, whereas the physical correlation length may be controlled by a different subleading eigenvalue. Local correlation functions uncover a cooperative rearrangement from charge-dominated to magnetically correlated regimes. Our results demonstrate that the sawtooth geometry promotes frustration and short-range coherence leading to pronounced pseudo-transition behavior.
Comments11 pages, 6 figures
