請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62217完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 高英哲(Ying-Jer Kao) | |
| dc.contributor.author | Yen-Chih Wang | en |
| dc.contributor.author | 王彥植 | zh_TW |
| dc.date.accessioned | 2021-06-16T13:34:27Z | - |
| dc.date.available | 2013-07-26 | |
| dc.date.copyright | 2013-07-26 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-18 | |
| dc.identifier.citation | [1] J Ignacio Cirac and Frank Verstraete. Renormalization and tensor product states in spin chains and lattices. Journal of Physics A: Mathematical and Theoretical, 42(50):
504004, 2009. [2] Kenneth G. Wilson. Renormalization group and critical phenomena. ii. phase-space cell analysis of critical behavior. Phys. Rev. B, 4:3184--3205, Nov 1971. [3] Steven R. White. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett., 69:2863--2866, Nov 1992. [4] Steven R. White. Density-matrix algorithms for quantum renormalization groups. Phys. Rev. B, 48:10345--10356, Oct 1993. [5] F. Verstraete and J. I. Cirac. Matrix product states represent ground states faithfully. Phys. Rev. B, 73:094423, Mar 2006. [6] Stellan Ostlund and Stefan Rommer. Thermodynamic limit of density matrix renormalization. Phys. Rev. Lett., 75:3537--3540, Nov 1995. [7] Guifre Vidal. Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett., 91:147902, Oct 2003. [8] V. Murg, F. Verstraete, and J. I. Cirac. Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states. Phys. Rev. A, 75:033605, Mar 2007. [9] G. Vidal. Entanglement renormalization. Phys. Rev. Lett., 99:220405, Nov 2007. 40 [10] Guifre Vidal. Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett., 91:147902, Oct 2003. [11] Guifre Vidal. Efficient simulation of one-dimensional quantum many-body systems. Phys. Rev. Lett., 93:040502, Jul 2004. [12] G. Vidal. Classical simulation of infinite-size quantum lattice systems in one spatial dimension. Phys. Rev. Lett., 98:070201, Feb 2007. [13] R. Orus and G. Vidal. Infinite time-evolving block decimation algorithm beyond unitary evolution. Phys. Rev. B, 78:155117, Oct 2008. [14] Pierre Pfeuty. The one-dimensional ising model with a transverse field. Annals of Physics, 57(1):79 -- 90, 1970. [15] Henk W. J. Blote and Youjin Deng. Cluster monte carlo simulation of the transverse ising model. Phys. Rev. E, 66:066110, Dec 2002. [16] Masuo Suzuki. Quantum monte carlo methods —recent developments. Physica A., 194(1–4):432 -- 449, 1993. [17] Masuo Suzuki. General theory of fractal path integrals with applications to many-body theories and statistical physics. J. Math. Phys., 32(2):400 -- 407, 1991. [18] Daniel Nagaj, Edward Farhi, Jeffrey Goldstone, Peter Shor, and Igor Sylvester. Quantum transverse-field ising model on an infinite tree from matrix product states. Phys. Rev. B, 77:214431, Jun 2008. [19] Y.-Y. Shi, L.-M. Duan, and G. Vidal. Classical simulation of quantum many-body systems with a tree tensor network. Phys. Rev. A, 74:022320, Aug 2006. [20] Michael Levin and Cody P. Nave. Tensor renormalization group approach to twodimensional classical lattice models. Phys. Rev. Lett., 99:120601, Sep 2007. [21] H. C. Jiang, Z. Y. Weng, and T. Xiang. Accurate determination of tensor network state of quantum lattice models in two dimensions. Phys. Rev. Lett., 101:090603, Aug 2008. 41 [22] Zheng-Cheng Gu, Michael Levin, and Xiao-Gang Wen. Tensor-entanglement renormalization group approach as a unified method for symmetry breaking and topological phase transitions. Phys. Rev. B, 78:205116, Nov 2008. [23] Zheng-Cheng Gu and Xiao-Gang Wen. Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order. Phys. Rev. B, 80:155131, Oct 2009. [24] Z. Y. Xie, J. Chen, M. P. Qin, J. W. Zhu, L. P. Yang, and T. Xiang. Coarsegraining renormalization by higher-order singular value decomposition. Phys. Rev. B, 86:045139, Jul 2012. [25] L. De Lathauwer, B. De Moor, and J. Vandewalle. A multilinear singular value decomposition. SIAM Journal on Matrix Analysis and Applications, 1(4):1253--1278, 2000. [26] M. J. D. Powell. An efficient method for finding the minimum of a function of several variables without calculating derivatives. The Computer Journal, 7(2):155--162, 1964. [27] Chen Liu, Ling Wang, Anders W. Sandvik, Yu-Cheng Su, and Ying-Jer Kao. Symmetry breaking and criticality in tensor-product states. Phys. Rev. B, 82:060410, Aug | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62217 | - |
| dc.description.abstract | 時間演化區塊消除法藉由時間演化來計算一個無限量子系統的基態，並經由測量此基態的能量或是磁化強度來研究此系統的相變化。此演算法在二維晶格上的直接推廣會因破壞原先的二維結構而無法得到令人滿意的結果。在此論文中我們提出了一種將二乘二小型方塊做為最小單位的改良；在計算時經由保留小型方塊內的量子糾纏，在鏈結維數為二的設定下，我們就已經能夠獲得比之前直接推廣的演算法還要更好的結果。 | zh_TW |
| dc.description.abstract | A recently developed algorithm called infinite time-evolving block decimation (iTEBD) allows us to calculate the ground state in simulated infinite quantum system through time evolution. With the ground state known, its corresponding energy or magnetization can be measured. From which the phase transition can also be studied. However, the conventional solution for the implementation of iTEBD on two-dimensional lattices fails to retain certain features and requires some improvements. In this thesis we propose a revision of the algorithm based on a two-by-two plaquette to the transverse Ising model on a 2D square lattice. The plqauette iTEBD takes the entanglement inside a plaquette fully into account. The comparison between the plaquette iTEBD and the conventional iTEBD shows that the former gives a better results than the latter with the smallest non-trivial bond dimension D=2. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T13:34:27Z (GMT). No. of bitstreams: 1 ntu-102-R99222077-1.pdf: 2095223 bytes, checksum: 0cf9464b68f873b3b1060a21e45c1c6b (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 致謝 . . . . . . . . . . . . . . . . . . . . . . . . . . i
中文摘要 . . . . . . . . . . . . . . . . . . . . . . . . ii Abstract . . . . . . . . . . . . . . . . . . . . . . . . iii Contents . . . . . . . . . . . . . . . . . . . . . . . . .iv List of Figures. . . . . . . . . . . . . . . . . . . . vi List of Tables . . . . . . . . . . . . . . . . . . . . . .viii 1 Introduction . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Transverse Ising Model . . . . . . . . . . . . . . . . 2 2 Matrix Product State . . . . . . . . . . . . . . . . . . 4 2.1 Fraction of the Hilbert space . . . . . . . . . . . . .4 2.2 Decomposition tools . . . . . . . . . . . . . . . . . .5 2.3 MPS in spin basis . . . . . . . . . . . . . . . . . . .7 3 Imaginary Time Evolving Block Decimation . . . . . . . .11 3.1 Imaginary Time Evolution . . . . . . . . . . . . . . 11 3.2 Updating the Matrices . . . . . . . . . . . . . . . . 13 3.3 Measurement of Wave Function . . . . . . . . . . . . 16 3.4 Summary of iTEBD algorithm for one-dimensional systems17 4 iTEBD on two-dimensional lattice . . . . . . . . . . . 19 4.1 Tree Geometry . . . . . . . . . . . . . . . . . . . . 19 4.2 Plaquette Update . . . . . . . . . . . . . . . . . . .22 4.3 Improvement on Measurement . . . . . . . . . . . . . .26 4.3.1 TRG . . . . . . . . . . . . . . . . . . . . . . . . 27 4.3.2 HOTRG . . . . . . . . . . . . . . . . . . . . . . . 30 4.3.3 Brute-force search with HOTRG . . . . . . . . . . . 34 5 Summary . . . . . . . . . . . . . . . . . . . . . . . . 37 Bibliography . . . . . . . . . . . . . . . . . . . . . . .40 | |
| dc.language.iso | en | |
| dc.subject | 窮舉法 | zh_TW |
| dc.subject | 矩陣積態 | zh_TW |
| dc.subject | 時間演化區塊消除法 | zh_TW |
| dc.subject | 小型方塊 | zh_TW |
| dc.subject | 張量重整化群 | zh_TW |
| dc.subject | matrix product state | en |
| dc.subject | tensor renormalization group | en |
| dc.subject | brute-force search | en |
| dc.subject | plaquette | en |
| dc.subject | infinite time-evolving block-decimation (iTEBD) | en |
| dc.title | 時間演化區塊消除法在二維正方易辛模型上的應用 | zh_TW |
| dc.title | Plaquette Infinite Time-evolving Block-Decimation Method for
the Transverse Ising Model on 2D Square Lattices | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳柏中(Po-Chung Chen),林豐利(Feng-Li Lin) | |
| dc.subject.keyword | 矩陣積態,時間演化區塊消除法,小型方塊,張量重整化群,窮舉法, | zh_TW |
| dc.subject.keyword | matrix product state,infinite time-evolving block-decimation (iTEBD),plaquette,tensor renormalization group,brute-force search, | en |
| dc.relation.page | 42 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-07-18 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 物理研究所 | zh_TW |
| 顯示於系所單位： | 物理學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-102-1.pdf 未授權公開取用 | 2.05 MB | Adobe PDF |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。