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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 高英哲(Ying-Jer Kao) | |
| dc.contributor.author | Yun-Hsuan Chou | en |
| dc.contributor.author | 周昀萱 | zh_TW |
| dc.date.accessioned | 2021-06-15T12:29:22Z | - |
| dc.date.available | 2016-09-01 | |
| dc.date.copyright | 2016-08-24 | |
| dc.date.issued | 2016 | |
| dc.date.submitted | 2016-08-05 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/50085 | - |
| dc.description.abstract | 如何判斷多體量子系統的相變化,且從微觀系統來得到巨觀上的物 理性質,在現代仍為凝態物理學中十分有趣的領域。
從 NRG 的為起點開始,多年來出現了許多突破性的演算法。其中 DMRG 在一維的系統的模擬中得到了相當好的結果。但在二微系統 中,因為 Area law 的關係使其表現不如在一微系統中精確,不僅如此, 在二維系統中,計算複雜度上升之速度也非一維系統可比擬。為了解 決這些問題,因而出現了許許多多不同的建立在張亮網路理論上的演 算法。 此篇論文,紀錄了幾個當今較為主流或新穎並用以模疑二維量子系 統的張亮網路演算法。一開始將簡單解釋張亮網路的基本理論; 再來會 介紹如何實做、優化演算法,以增加精確度和降低計算複雜度。章節 中也附上偽代碼,來說明實作中應注意之細節。最後會比較它們計算 二維易辛模型與海森堡模型的結果,來說明各演算法之優缺點。 | zh_TW |
| dc.description.abstract | Determining the phase transition of many body systems and the physi- cal properties of macroscopic systems from microscopic description are still challenging in condense matter physics.
Since the numerical renormalization group (NRG) came out, various al- gorithms sprang up like mushrooms for analyzing these problems . Among all, the density matrix renormalization group (DMRG) could be considered as the most remarkable outcome, which analyze accurately in one dimensional systems. However, it perform worse in two dimensional systems. Not only the physical reasons, such as the area law, but also the rapid increment of computational complexity which is much higher than in one dimensional sys- tems. In order to study the phenomenals in twe-dimensional systems. First of all, we briefly introduce the tensor network theory. Secondly, we recorded some of popular tensor network algorithms which are developed for handling the problems in two-dimensional systems. Furthermore, the network diagrams and pseudo-code are presented, which gives the instruction of how to imple- ment these algorithms. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T12:29:22Z (GMT). No. of bitstreams: 1 ntu-105-R02222062-1.pdf: 5358098 bytes, checksum: b819f47654628448458e2690e401c5ef (MD5) Previous issue date: 2016 | en |
| dc.description.tableofcontents | 致謝 iii
摘要 iv Abstract v 1 Introduction 1 1.1 Overview 1 2 Tensor Network Theory 3 2.1 Representation of tensors in tensor Networks 3 2.2 Tensor operations and tensor network diagrams 4 2.2.1 Permutation 4 2.2.2 Reshape 5 2.2.3 Tensor contraction 5 2.3 Quantum state as a tensor network 7 2.4 Matrix product state 8 2.5 Projected entangled pair state 10 3 2D Imaginary Time Evolving Block Decimation 11 3.1 Imaginary Time Evolution 12 3.1.1 One dimensional infinite imaginary-time evolving block decimation 13 3.2 Infinite Imaginary-Time Evolving Block Decimation for 2D system 16 3.2.1 Two-dimensional iTEBD 16 3.3 Improvement a la Hastings 18 3.4 Optimizations 20 3.4.1 Initialization 20 3.4.2 QR and LQ decomposition 21 3.4.3 Truncation Error 25 3.5 Comparison 25 3.5.1 Different Initializations 25 3.5.2 Different schemes of 2D-iTEBD 26 3.6 Cut off of the truncation error 28 4 Infinite Projected Entangled Simplex State 30 4.1 Simplex-solid State 30 4.2 Variational PESS ansatz 33 4.2.1 High-order singular value decomposition 33 4.2.2 Simple update for PESS 35 4.3 Infinite Kagome lattice 36 4.3.1 3-PESS 36 4.3.2 5-PESS 40 4.4 Infinite Square lattice 42 4.4.1 4-PESS(Rank-3projectiontensors) 42 4.5 Properties of PESS algorithm 44 4.5.1 3PESS on infinite Kagome lattice 44 4.5.1.1 S=1 45 4.5.1.2 S=2 46 4.5.2 4-PESS for Heisenberg model on square lattice 48 5 Corner Transfer Matrix 50 5.1 Obtain States from PEPS 51 5.2 Obtain States from PESS 55 5.3 Comparison 56 6 Summary 58 Bibliography 60 | |
| dc.language.iso | en | |
| dc.subject | 邊角移矩陣 | zh_TW |
| dc.subject | 投影糾纏單態 | zh_TW |
| dc.subject | 無限時間演化區塊 | zh_TW |
| dc.subject | 張量重整化群 | zh_TW |
| dc.subject | 矩陣基態 | zh_TW |
| dc.subject | 投影糾纏對態 | zh_TW |
| dc.subject | projected entangled pair state(PEPS) | en |
| dc.subject | matrix product state(MPS) | en |
| dc.subject | tensor renormalization group | en |
| dc.subject | corner transfer matrix | en |
| dc.subject | infinite time-evolveing block-decimation | en |
| dc.subject | projected entangled simplex state | en |
| dc.title | 比較不同張量網路演算法應用在二微多體量子物理系統之優劣 | zh_TW |
| dc.title | Comparative Studies of Tensor Network Algorithms for Two Dimensional Quantum Many-Body Systems | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 104-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 林瑜琤(Yu-cheng Lin),陳柏中(Po-chung Chen) | |
| dc.subject.keyword | 矩陣基態,投影糾纏對態,投影糾纏單態,無限時間演化區塊,邊角移矩陣,張量重整化群, | zh_TW |
| dc.subject.keyword | matrix product state(MPS),projected entangled pair state(PEPS),projected entangled simplex state,infinite time-evolveing block-decimation,corner transfer matrix,tensor renormalization group, | en |
| dc.relation.page | 62 | |
| dc.identifier.doi | 10.6342/NTU201601956 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2016-08-07 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理學研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
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