Title

張量網狀態在二維量子自旋系統的應用

Translated Titles

Tensor Network States in Two Dimensional Quantum Spin Systems

DOI

10.6342/NTU.2010.01079

Authors

蕭信智

Key Words

張量網狀態 ; 調變原理 ; 最佳化 ; 重整化群 ; 挫折性系統 ; tensor network states ; variational principle ; optimization ; renormalization group ; frustrated systems

PublicationName

臺灣大學物理研究所學位論文

Volume or Term/Year and Month of Publication

2010年

Academic Degree Category

碩士

Advisor

高英哲

Content Language

英文

Chinese Abstract

張量網狀態 (tensor network states)可作為研究量子自旋系統基態的試驗波函數。在這一篇論文裡,我們介紹兩種方法,為張量糾纏重整化群 (tensor entanglement renormalization group)及方磚重整法 (plaquette renormalization scheme)。張量糾纏重整化群使用張量乘積態 (tensor product states)做為試驗波函數且為了有效率的計算做了估計。方磚重整法使用方磚重整態 (plaquette renormalized states)做為試驗波函數而不需要做估計。我們使用二維的伊辛模型 (Ising model)來驗證這些方法我們發現張量糾纏重整化群在相對直接對角化 (exact diagonalization)的大尺寸下可使用。藉由使用方磚重整態,我們能夠有信心地找出量子自旋系統的基態。

English Abstract

Tensor network states can be used as a trial wave function to study ground states for quantum spin systems. In this thesis, we introduce two methods, tensor entanglement renormalization group (TERG) method and plaquette renormalization scheme. TERG uses tensor product states as a trial wave function and does an approximation for efficient calculations. Plaquette renormalization scheme uses plaquette renormalized states as a trial wave function without approximate procedures. We demonstrate these methods with two dimensional transverse Ising model. It’s shown that TERG works in a large size compared to exact diagonalization. By using plaquette renormalized states, we can represent ground states faithfully for frustrated spin systems.

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