自旋子的量子临界性
Quantum criticality of spinons
摘要：
一维自旋链中相互作用自旋的自由费米子性质仍然缺乏严格的研究。在这封信中，我们表明，长度为$1$的自旋弦显着支配的自旋子，磁振子和自由费米子的临界性质的一维反铁磁自旋1/2链。我们使用Bethe的量子力学解解析地计算了模型的热性质和磁性质的精确标度函数，从而对自旋子的量子临界性有了严格的理解。事实证明，比热的双峰优雅地标记了从临界点向外散开的两个交叉温度，表明三个量子相：Tomonaga-Luttinger液体（TLL），量子临界和完全极化的铁磁相。对于TLL相，威尔逊比$R_W=4K_s$保持几乎与温度无关，这里$K_s$是Luttinger参数。此外，应用我们的结果，我们精确地确定了量子标度和临界指数的所有磁性在理想的一维自旋1/2反铁磁体Cu（C ${}_4$ H ${}_4$ N ${}_2$）（NO ${}_3$）${}_2$最近在物理评论Lett。{ \bf 114}，037202（2015）]。我们进一步发现，在实验中使用的磁化峰是不是一个很好的量来映射有限温度TLL相界。
英文摘要：
The free fermion nature of interacting spins in one dimensional (1D) spin chains still lacks a rigorous study. In this letter we show that the length-$1$ spin strings significantly dominate critical properties of spinons, magnons and free fermions in the 1D antiferromagnetic spin-1/2 chain. Using the Bethe ansatz solution we analytically calculate exact scaling functions of thermal and magnetic properties of the model, providing a rigorous understanding of the quantum criticality of spinons. It turns out that the double peaks in specific heat elegantly mark two crossover temperatures fanning out from the critical point, indicating three quantum phases: the Tomonaga-Luttinger liquid (TLL), quantum critical and fully polarized ferromagnetic phases. For the TLL phase, the Wilson ratio $R_W=4K_s$ remains almost temperature-independent, here $K_s$ is the Luttinger parameter. Furthermore, applying our results we precisely determine the quantum scalings and critical exponents of all magnetic properties in the ideal 1D spin-1/2 antiferromagnet Cu(C${}_4$H${}_4$N${}_2$)(NO${}_3$)${}_2$ recently studied in Phys. Rev. Lett. {\bf 114}, 037202 (2015)]. We further find that the magnetization peak used in experiments is not a good quantity to map out the finite temperature TLL phase boundary.
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