AI 中文总结
研究表明更高贝里曲率可计算量子自旋链中纠缠切割产生的无隙边缘模式，定义整数值拓扑序参量。通过构建扩展族等方法，其积分与贝里相位相关，能计数边缘模式自旋，值变标志相变，并用多个自旋链实例加以说明。
AI 中文摘要
我们表明，更高贝里曲率（HBC）可用于计算由纠缠切割产生的无隙边缘模式，从而为量子自旋链定义一个整数值拓扑序参量。给定单个自旋链哈密顿量，通过插值到参考乘积涅耳态构建一个扩展族，并表明HBC在此扩展上的积分等于链的一半响应无穷小场扫过的普通贝里相位。它计算切割暴露的无隙边缘模式的自旋，其整数值的变化标志着相变。我们用几个例子说明这一点：\(S = 1/2\)、\(S = 1\)和\(S = 3/2\)自旋 - 佩尔斯链，它们在不同二聚化模式之间经历“单重态翻转”转变；双线性 - 双二次链，阐明与严格对称保护拓扑相分类的联系；以及交错\(J_1 - J_2\)链，其单重态的最近邻和第三邻模式取决于相互作用的符号。
英文摘要
We show that the higher Berry curvature (HBC) can be used to count the gapless edge modes created by an entanglement cut, and thus defines an integer-valued topological order parameter for quantum spin chains. Given an individual spin-chain Hamiltonian, we construct an extending family by interpolating to a reference product Néel state, and show that the integral of the HBC over this extension is equal to the ordinary Berry phase of half of the chain swept out in response to an \textit{infinitesimal} field. It thus counts the spin of the gapless edge modes exposed by the cut, and a change in its integer value signals a phase transition. We illustrate this with several examples: $S=1/2$, $S=1$, and $S=3/2$ spin-Peierls chains, which undergo `singlet flop' transitions between different patterns of dimerisation; the bilinear-biquadratic chain, which clarifies the connection to the strict symmetry-protected topological phases classification; and the staggered $J_1$--$J_2$ chain, which has both nearest-neighbour and third-neighbour patterns of singlets depending on the signs of the interactions.
Comments10.5 pages, 6 figures
