AI 中文总结
研究带额外近邻相互作用的团簇伊辛链，通过张量网络和弱耦合场论发现其存在临界分岔、退禁闭量子临界线等新相及相变，满足八顶点普适类关系，还存在平移对称性破缺反铁磁体。
AI 中文摘要
我们采用张量网络方法和弱耦合场论研究带有额外近邻相互作用的团簇伊辛链。若无相互作用，Jordan-Wigner变换将该模型分解为由精确O(3)味对称性关联的三条相同的马约拉纳链。它们的共同质量在SU(2)₂ Wess-Zumino-Novikov-Witten临界点处消失，该临界点的中心电荷c=3/2，将对称性保护的拓扑团簇相与铁磁体分隔开。该相互作用将O(3)约化为其循环子群C₃，使三条链分裂为一个单态和一个二重态，二者的能隙分别闭合，产生临界分岔，形成伊辛（c=1/2）和高斯（c=1）临界线。在这些临界线之间，排斥相互作用会产生第二个铁磁相，吸引相互作用则产生无序相。高斯线随后分隔了两个朗道不相容的铁磁体，实现了具有涌现O(2)对称性的退禁闭量子临界线，沿该线我们独立提取的指数连续变化，但满足八顶点弱普适类的无参数关系β=(2ν-1)/4。在更强的排斥作用下，该线会扩展为具有非公度代数关联的扩展无隙漂浮相，通过Berezinskii-Kosterlitz-Thouless相变进入该相。所有这些相及其之间的相变都可被弱耦合理论捕捉。超出其适用范围后，我们的模拟揭示了通过一级相变达到的平移对称性破缺反铁磁体。
英文摘要
We investigate the cluster Ising chain with an additional nearest-neighbor interaction using tensor-network methods and a weak-coupling field theory. Without the interaction, the Jordan-Wigner transformation decomposes the model into a triplet of identical Majorana chains related by an exact $O(3)$ flavor symmetry. Their common mass vanishes at the $SU(2)_2$ Wess-Zumino-Novikov-Witten critical point with central charge $c = 3/2$ separating the symmetry-protected topological cluster phase from a ferromagnet. The interaction reduces $O(3)$ to its cyclic subgroup $C_3$, splitting the triplet into a singlet and a doublet whose gaps close separately, producing a critical bifurcation into Ising ($c = 1/2$) and Gaussian ($c = 1$) critical lines. A second ferromagnetic phase opens between these critical lines for repulsive interactions and a disordered phase for attractive ones. The Gaussian line then separates two Landau-incompatible ferromagnets, realizing a deconfined quantum critical line with emergent $O(2)$ symmetry, along which our independently extracted exponents vary continuously yet satisfy the parameter-free relation $β= (2ν- 1)/4$ of the eight-vertex weak universality class. At stronger repulsion this line opens into an extended gapless floating phase with incommensurate algebraic correlations, entered through Berezinskii-Kosterlitz-Thouless transitions. All of these phases and the transitions between them are captured by the weak-coupling theory. Beyond its regime of validity, our simulations reveal a translation-symmetry-breaking antiferromagnet reached through first-order transitions.
Comments21 pages, 8 figures, comments are welcome
