一维ANNNI模型中MPS的有限纠缠标度研究相变
Exploring phase transitions by finite-entanglement scaling of MPS in the 1D ANNNI model
摘要：
我们使用无限矩阵乘积态（iMPS）的有限纠缠标度来探索所谓的无限阶跃。这种通用方法可以具有比有限尺寸标度更低的计算成本。为此，我们研究了可能的MPS为基础的算法，以找到基态的横轴次近邻伊辛（ANNNI）模型的自旋链与第一和第二邻居相互作用和挫折。基态有四个不同的阶段，过渡的二阶和一个假定的无限阶，Kosterlitz无相变。为了探索该模型中的相变，我们研究了相关长度、纠缠熵和能量对外场的二阶导数等一般量，并检验了有限纠缠标度.我们提出了一个非临界系统的关联长度的标度系数，以探索无限阶跃。与[8]中的有限尺寸标度方法相比，该方法提供了相当少的计算成本，并且省略了通过应用固定边界条件（例如[8]中的畴壁能量）获得的量。结果表明，良好的协议与以前的研究有限尺寸标度使用DMRG。
英文摘要：
We use the finite-entanglement scaling of infinite matrix product states (iMPS) to explore supposedly infinite order transitions. This universal method may have lower computational costs than finite-size scaling. To this end, we study possible MPS-based algorithms to find the ground states of the transverse axial next-nearest-neighbor Ising (ANNNI) model in a spin chain with first and second neighbor interactions and frustration. The ground state has four distinct phases with transitions of second order and one of supposedly infinite order, the Kosterlitz-Thouless transition. To explore phase transitions in the model, we study general quantities such as the correlation length, entanglement entropy and the second derivative of the energy with respect to the external field, and test the finite-entanglement scaling. We propose a scaling ansatz for the correlation length of a non-critical system in order to explore infinite order transitions. This method provides considerably less computational costs compared to the finite-size scaling method in [8], and quantities obtained by applying fixed boundary conditions (such as domain wall energy in [8]) are omitted. The results show good agreement with previous studies of finite-size scaling using DMRG.
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