使Fredkin自旋链变形远离其无挫折点
Deforming the Fredkin spin chain away from its frustration-free point
摘要：
Fredkin模型描述了一个受三体、相关交换相互作用和扭曲边界条件影响的自旋半链段。该模型是无阻挫的，其基态波函数是精确已知的。它的低能物理是一个强xy铁磁体，具有无隙激发和异常大的动力学指数。我们研究了一个广义的自旋链模型，其中包括Fredkin模型作为一个特殊的调谐点，否则传统的铁磁和反铁磁量子海森堡模型之间的插值。我们解决的低洼状态，使用精确的对角化和密度矩阵重整化群计算，为了跟踪系统的属性，因为它是从Fredkin点调谐;我们还提出了精确的分析结果，在Fredkin点举行。我们确定了一个零温度相图与多个过渡和意想不到的有序相。Fredkin的基态被证明是特别脆弱的，即使是无穷小的反铁磁挫折也不稳定。我们注意到存在一个“反Fredkin”点，在该点上所有的贡献自旋配置有一个自旋结构完全相反的Fredkin基态。
英文摘要：
The Fredkin model describes a spin-half chain segment subject to three-body, correlated-exchange interactions and twisted boundary conditions. The model is frustration-free, and its ground state wave function is known exactly. Its low-energy physics is that of a strong xy ferromagnet with gapless excitations and an unusually large dynamical exponent. We study a generalized spin chain model that includes the Fredkin model as a special tuning point and otherwise interpolates between the conventional ferromagnetic and antiferromagnetic quantum Heisenberg models. We solve for the low-lying states, using exact diagonalization and density-matrix renormalization group calculations, in order to track the properties of the system as it is tuned away from the Fredkin point; we also present exact analytical results that hold right at the Fredkin point. We identify a zero-temperature phase diagram with multiple transitions and unexpected ordered phases. The Fredkin ground state turns out to be particularly brittle, unstable to even infinitesimal antiferromagnetic frustration. We remark on the existence of an "anti-Fredkin" point at which all the contributing spin configurations have a spin structure exactly opposite to those in the Fredkin ground state.
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