论文标题
XY自旋链中交错磁化和域壁的完整计数统计
Exact full counting statistics for the staggered magnetization and the domain walls in the XY spin chain
论文作者
论文摘要
对于XY自旋链的有限间隔，我们计算横向，交错磁化和域壁的横向，交错磁化和域壁的累积生成函数（完整计数统计）。特别是，我们还以横向磁化的完整计数统计量和基于PainlevéV方程的解决方案的整体计数统计量来得出一个通用插值公式。通过进一步确定大间隔渐近学的转基准校正，我们能够测试临界时保形场理论预测的适用性。作为副产品，我们还获得了确切的结果，即在$σ^z $和$σ^z $和$σ^x $基础基础上形成铁磁和反铁磁域的可能性。该分析取决于块状toeplitz决定因素的渐近扩展，为此我们以数值为单位进行了新的猜想。
We calculate exactly cumulant generating functions (full counting statistics) for the transverse, staggered magnetization and the domain walls at zero temperature for a finite interval of the XY spin chain. In particular, we also derive a universal interpolation formula in the scaling limit for the full counting statistics of the transverse magnetization and the domain walls which is based on the solution of a Painlevé V equation. By further determining subleading corrections in a large interval asymptotics, we are able to test the applicability of conformal field theory predictions at criticality. As a byproduct, we also obtain exact results for the probability of formation of ferromagnetic and antiferromagnetic domains in both $σ^z$ and $σ^x$ basis in the ground state. The analysis hinges upon asymptotic expansions of block Toeplitz determinants, for which we formulate and check numerically a new conjecture.
