Title

張量網路演算法對Thirring 模型在一維無限長格點之研究

Translated Titles

Tensor Network Studies of Thirring Model on a One-dimensional Infinite-size Lattice

DOI

10.6342/NTU201802766

Authors

洪浩迪

Key Words

張量網路 ; 矩陣乘積態 ; 均勻矩陣乘積態的變分優化演算法 ; 時間相依變分原理 ; Tirring 模型 ; 量子演化 ; 動態相變 ; tensor network (TN) ; matrix product state (MPS) ; variational optimization algorithm for uniform matrix product state (VUMPS) ; time-dependent variational principle (TDVP) ; Thirring model ; quantum quench ; dynamical phase transition (DPT)

PublicationName

臺灣大學物理學研究所學位論文

Volume or Term/Year and Month of Publication

2018年

Academic Degree Category

碩士

Advisor

高英哲

Content Language

英文

Chinese 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。

English Abstract

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.

Topic Category 基礎與應用科學 > 物理
理學院 > 物理學研究所
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