張量網路演算法對Thirring 模型在一維無限長格點之研究

Abstract

我們利用張量網路演算法研究Thirring 模型。我們將模型離散化後，找出Thirring 模型哈密頓的自旋算符表示法並用矩陣作用算符表示。 利用均勻矩陣乘積態的變分優化演算法去找出模型的基態解並調查其相圖。然後利用時間相依變分原理來研究Thirring 模型的動態演化，特別是對於跨相變的動態演化特別有興趣。

We use tensor networks to study the Thirring model. We discretize the model onto the lattice, find the spin representation for the Hamiltonian of the Thirring model and use the matrix product operator (MPO) to represent it. Using the variational optimization algorithms for uniform Matrix Product State (VUMPS), we find the ground state of the model and investigate the phase diagram. Then, we use the time-dependent variational principle algorithm (TDVP) to study the quench dynamics for the Thirring model, especially for what happens when quenching different phases.