论文标题
Quantum XY自旋链中的形成概率和通用边界熵的缩放
Scaling of the Formation Probabilities and Universal Boundary Entropies in the Quantum XY Spin Chain
论文作者
论文摘要
我们准确地计算出在给定的旋转配置中以横向$σ^z $ -BOSIS中给定的旋转配置找到XY链的基态的概率。通过确定有限体积校正到多种配置的概率，我们在临界点获得了通用边界熵。后者是表征每个量子状态的基础边界综合场理论的基准。为了确定概率的缩放率，我们证明了一个定理，以分解形式表达循环矩阵的子矩阵的特征值作为原始矩阵特征值的函数。最后，通过利用Euler-Maclaurin公式对非差异功能的概括来计算边界熵。结果表明，在某些情况下，旋转构型可以流向Cardy状态的线性叠加。我们的方法和工具是相当通用的，可以应用于所有定期量子链中，这些量子链将其映射到自由用的汉密尔顿人。
We calculate exactly the probability to find the ground state of the XY chain in a given spin configuration in the transverse $σ^z$-basis. By determining finite-volume corrections to the probabilities for a wide variety of configurations, we obtain the universal Boundary Entropy at the critical point. The latter is a benchmark of the underlying Boundary Conformal Field Theory characterizing each quantum state. To determine the scaling of the probabilities, we prove a theorem that expresses, in a factorized form, the eigenvalues of a sub-matrix of a circulant matrix as functions of the eigenvalues of the original matrix. Finally, the Boundary Entropies are computed by exploiting a generalization of the Euler-MacLaurin formula to non-differentiable functions. It is shown that, in some cases, the spin configuration can flow to a linear superposition of Cardy states. Our methods and tools are rather generic and can be applied to all the periodic quantum chains which map to free-fermionic Hamiltonians.
