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研究生： 王國霖
Wang, Kuo-Lin
論文名稱： Field-Induced Phase Transition in the Frustrated Bilayer Model
二聚化錯亂模型在外場引發下的相變行為
指導教授： 陳柏中
Chen, Po-Chung
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 物理學系
Department of Physics
論文出版年： 2010
畢業學年度： 98
語文別： 英文
論文頁數： 31
中文關鍵詞： 反鐵磁 、超流體
外文關鍵詞： superfliud, supersolid, dimer
相關次數： 點閱：5  下載：0 
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    • Abstract
    In recent years, spin-1/2 dimerized antiferromagnets have become
    a remarkable subject since rich eld-induced quantum phases
    can appear. In this work, we study second order quantum phase
    transition caculated by this combined algorithm of the innite timeevolving
    block decimation method and tensor renormalization group
    approach. By applying an enough magnetic eld, a spin superuid
    phase is observed. Moreover, a supersolid phase is also observed in
    small regime of magnetic eld. We will show the full phase diagrams
    in various weaker frustrating interlayer interaction.

    1 Introduction 4 2 The Dimerized Antiferromagnets 6 2.1 The Hamiltonian and Order Parameter . . . . . . . . . . . . . . . 6 2.2 Bosonic Property and Superuid phase . . . . . . . . . . . . . . . 8 2.3 SuperSolid Phase . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 3 Numerical Approach 10 3.1 Tensor Product State . . . . . . . . . . . . . . . . . . . . . . . . . 10 3.1.1 Conceptual Aspects of Tensor Product State . . . . . . . 10 3.1.2 2-D Tensor Product State . . . . . . . . . . . . . . . . . . 12 3.2 The Innite Time-evolving Block Decimation Method . 13 3.2.1 Imaginary Time Evolution and Trotter-Suzuki Decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 3.2.2 Construct the Hamiltonian . . . . . . . . . . . . . . . . . 13 3.2.3 Applying Gate on TPS . . . . . . . . . . . . . . . . . . . 15 3.3 The Tensor Renormalization-group Approach . . . . . . . . . . . 18 3.3.1 Construct the Double Tensor . . . . . . . . . . . . . . . . 18 3.3.2 TRG Coarse-graining . . . . . . . . . . . . . . . . . . . . 19 4 The Phase Diagram with Dierent Frustration 20 4.1 The Performance of TPS within Phase Transition Region . . . . 20 4.1.1 The Dependence of Bond Dimention D . . . . . . . . . . 20 4.1.2 Energy Spectrum . . . . . . . . . . . . . . . . . . . . . . . 21 4.2 Full Phase Diagram . . . . . . . . . . . . . . . . . . . . . . . . . 22 4.2.1 Some Critical Case . . . . . . . . . . . . . . . . . . . . . . 22 4.2.2 Phase Diagram and Comparison of Other Results . . . . 24 5 Conclusion and Outlook 26 A Schmidt Decomposition 27 B Singular Value Decomposition 28

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