臺灣博碩士論文加值系統

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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