论文标题
在波动矩阵乘积状态下，自旋1链的路径积分
Path Integral for Spin-1 Chain in the Fluctuating Matrix Product State Basis
论文作者
论文摘要
引入了一种新的写入Spin-1 Heisenberg抗磁磁链的路径积分的方法。代替导致非线性Sigma模型的常规连贯状态，我们使用了一个新的基础，称为波动矩阵乘积状态（FMP），从一开始就体现了地点间纠缠。它形成了跨越自旋-1链的整个希尔伯特空间的过度套装。对双线性 - 生物旋转模型进行的鞍点分析预测了Aklt Hamiltonian附近的基态，预测了Affeck-Kennedy-lieb-tasaki（AKLT）状态。通过围绕马鞍点梯度扩展得出的二次有效作用，不受困扰非线性Sigma模型并完全可解决的约束。获得的激发模式与AKLT Hamiltonian的单模近似结果完全一致。通过对角二次作用，还获得了其他BLBQ汉密尔顿人的激发光谱。
A new method of writing down the path integral for spin-1 Heisenberg antiferromagnetic chain is introduced. In place of the conventional coherent state basis that leads to the non-linear sigma-model, we use a new basis called the fluctuating matrix product states (fMPS) which embodies inter-site entanglement from the outset. It forms an overcomplete set spanning the entire Hilbert space of the spin-1 chain. Saddle-point analysis performed for the bilinear-biquadratic spin model predicts Affeck-Kennedy-Lieb-Tasaki (AKLT) state as the ground state in the vicinity of the AKLT Hamiltonian. Quadratic effective action derived by gradient expansion around the saddle point is free from constraints that plagued the non-linear sigma model and exactly solvable. The obtained excitation modes agree precisely with the single-mode approximation result for the AKLT Hamiltonian. Excitation spectra for other BLBQ Hamiltonians are obtained as well by diagonalizing the quadratic action.
