Accurate determination of the Gaussian transition in spin-1 chains with single-ion anisotropy
Accurate determination of the Gaussian transition in spin-1 chains with single-ion anisotropy
复制标题
利用单离子各向异性准确测定自旋 1 链中的高斯跃迁
DOI：
10.1103/physrevb.84.220402
复制
发表时间：
2011-12-02
影响因子：
3.7
通讯作者：
Yu, Lu
中科院分区：
文献类型：
--
作者：
Hu, Shijie;Normand, B.;Yu, Lu
具有单离子各向异性的自旋一海森堡链中的高斯转变无论在分析上还是在数值上都极其难以处理。我们引入了具有严格错误控制的改进的 DMRG 程序，我们用它来访问非常大的系统。通过考虑体熵，我们确定了 4 位精度的高斯转变点 $D_{c}/J
= 0.96845(8)$，解决了量子磁性中长期存在的争论。利用这个值，我们获得了包括基态能量、能隙和横向弦序参数在内的量的临界行为的高精度数据，以及临界指数$\nu = 1.472(2)$。在 $J_{z} = 0.5$ 处应用我们改进的技术突出了沿高斯过渡线的关键行为的本质差异。
The Gaussian transition in the spin-one Heisenberg chain with single-ion anisotropy is extremely difficult to treat, both analytically and numerically. We introduce an improved DMRG procedure with strict error control, which we use to access very large systems. By considering the bulk entropy, we determine the Gaussian transition point to 4-digit accuracy, $D_{c}/J
= 0.96845(8)$, resolving a long-standing debate in quantum magnetism. With this value, we obtain high-precision data for the critical behavior of quantities including the ground-state energy, gap, and transverse string-order parameter, and for the critical exponent, $\nu = 1.472(2)$. Applying our improved technique at $J_{z} = 0.5$ highlights essential differences in critical behavior along the Gaussian transition line.