论文标题
构建Heisenberg Spin-1链的变分基质产品状态
Construction of Variational Matrix Product States for the Heisenberg Spin-1 Chain
论文作者
论文摘要
我们提出了一个简单的变分波函数，该函数将Spin-1 Heisenberg链模型的正确基态能量捕获到0.04 \％以内。波函数以矩阵乘积状态（MPS）形式编写，其键尺寸$ d = 8 $，并以三个伪善参数为特征。拟议的MPS通过将二聚体，三聚体和一般$ Q $ dimers穿衣来概括了Affleck-Kennedy-Lieb-Tasaki（AKLT）状态。逃逸参数控制$ q $ -mers的数字和平均大小。此外，$ d = 8 $变异国会议员州捕获了属于Haldane阶段的整个双线性 - 生物 - 生物 - 生物学哈密顿族的基态。发现我们MPS状态的纠缠光谱中的2-4-2退化结构与密度基质重质化组（DMRG）计算的结果非常匹配，该计算在计算上重得多。自旋旋转相关函数还可以与DMRG获得的功能非常拟合。
We propose a simple variational wave function that captures the correct ground state energy of the spin-1 Heisenberg chain model to within 0.04\%. The wave function is written in the matrix product state (MPS) form with the bond dimension $D=8$, and characterized by three fugacity parameters. The proposed MPS generalizes the Affleck-Kennedy-Lieb-Tasaki (AKLT) state by dressing it with dimers, trimers, and general $q$-dimers. The fugacity parameters control the number and the average size of the $q$-mers. Furthermore, the $D=8$ variational MPS state captures the ground states of the entire family of bilinear-biquadratic Hamiltonian belonging to the Haldane phase to high accuracy. The 2-4-2 degeneracy structure in the entanglement spectrum of our MPS state is found to match well with the results of density matrix renormalization group (DMRG) calculation, which is computationally much heavier. Spin-spin correlation functions also find excellent fit with those obtained by DMRG.
