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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 高英哲(Ying-Jer Kao) | |
| dc.contributor.author | Hao-Ti Hung | en |
| dc.contributor.author | 洪浩迪 | zh_TW |
| dc.date.accessioned | 2021-05-12T09:32:50Z | - |
| dc.date.available | 2018-08-09 | |
| dc.date.available | 2021-05-12T09:32:50Z | - |
| dc.date.copyright | 2018-08-09 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-08-08 | |
| dc.identifier.citation | [1] R. Orús, “A practical introduction to tensor networks: Matrix product states and projected entangled pair states,” Annals of Physics, vol. 349, pp. 117 – 158, 2014.
[2] U. Schollwöck, “The density-matrix renormalization group in the age of matrix product states,” Annals of Physics, vol. 326, no. 1, pp. 96 – 192, 2011. January 2011 Special Issue. [3] S. R. White, “Density matrix formulation for quantum renormalization groups,” Phys. Rev. Lett., vol. 69, pp. 2863–2866, Nov 1992. [4] G. Vidal, “Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension,” Phys. Rev. Lett., vol. 98, p. 070201, Feb 2007. [5] V. Zauner-Stauber, L. Vanderstraeten, M. T. Fishman, F. Verstraete, and J. Haegeman, “Variational optimization algorithms for uniform matrix product states,” Phys. Rev. B, vol. 97, p. 045145, Jan 2018. [6] J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, “Time-Dependent Variational Principle for Quantum Lattices,” Phys. Rev. Lett., vol. 107, p. 070601, Aug 2011. [7] H. N. Phien, G. Vidal, and I. P. McCulloch, “Infinite boundary conditions for matrix product state calculations,” Phys. Rev. B, vol. 86, p. 245107, Dec 2012. [8] M. Heyl, “Dynamical quantum phase transitions: a review,” Reports on Progress in Physics, vol. 81, no. 5, p. 054001, 2018. [9] Mari Carmen Bañuls, Krzysztof Cichy , Ying-Jer Kao, C.-J. David Lin, Yu-Ping Lin, and David Tao-Lin Tan , “Tensor Network study of the (1+1)-dimensional Thirring Model,” EPJ Web Conf., vol. 175, p.11017, 2018. [10] T. Banks, L. Susskind, and J. Kogut, “Strong-coupling calculations of lattice gauge theories: (1 + 1)-dimensional exercises,” Phys. Rev. D, vol. 13, pp. 1043–1053, Feb 1976. [11] F. C. Alcaraz and A. L. Malvezzi, “Critical and off-critical properties of the XXZ chain in external homogeneous and staggered magnetic fields,” Journal of Physics A: Mathematical and General, vol. 28, no. 6, p.1521, 1995. [12] M. Bañuls, K. Cichy, J. Cirac, and K. Jansen, “The mass spectrum of the Schwinger model with matrix product states,” Journal of High Energy Physics, vol. 2013, p. 158, Nov 2013. [13] J. M. Kosterlitz and D. J. Thouless, “Ordering, metastability and phase transitions in two-dimensional systems,” Journal of Physics C: Solid State Physics, vol. 6, no. 7, p. 1181, 1973. [14] V. L. Berezinskiǐ, “Destruction of Long-range Order in One-dimensional and Two-dimensional Systems having a Continuous Symmetry Group I. Classical Systems,” Soviet Journal of Experimental and Theoretical Physics, vol. 32, p. 493, 1971. [15] R. Orús and G. Vidal, “Infinite time-evolving block decimation algorithm beyond unitary evolution,” Phys. Rev. B, vol. 78, p. 155117, Oct 2008. [16] H. van der Vorst, “Bi-CGSTAB: A Fast and Smoothly Converging Variant of Bi-CG for the Solution of Nonsymmetric Linear Systems,” SIAM Journal on Scientific and Statistical Computing, vol. 13, no. 2, pp. 631–644, 1992. [17] R. Bhatia, Matrix Analysis. Springer-Verlag, 1997. Thm. IX.7.2,R. [18] J. C. Halimeh and V. Zauner-Stauber, “Dynamical phase diagram of quantum spin chains with long-range interactions,” Phys. Rev. B, vol. 96, p. 134427, Oct 2017. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/handle/123456789/1118 | - |
| dc.description.abstract | 我們利用張量網路演算法研究Thirring 模型。我們將模型離散化後，找出Thirring 模型哈密頓的自旋算符表示法並用矩陣作用算符表示。
利用均勻矩陣乘積態的變分優化演算法去找出模型的基態解並調查其相圖。然後利用時間相依變分原理來研究Thirring 模型的動態演化，特別是對於跨相變的動態演化特別有興趣。 | zh_TW |
| dc.description.abstract | We use tensor networks to study the Thirring model. We discretize the model onto the lattice, find the spin representation for the Hamiltonian of the Thirring model and use the matrix product operator (MPO) to represent it.
Using the variational optimization algorithms for uniform Matrix Product State (VUMPS), we find the ground state of the model and investigate the phase diagram. Then, we use the time-dependent variational principle algorithm (TDVP) to study the quench dynamics for the Thirring model, especially for what happens when quenching different phases. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-12T09:32:50Z (GMT). No. of bitstreams: 1 ntu-107-R05222034-1.pdf: 10506071 bytes, checksum: a4abd38163ea089a91be26f77fe8cb2d (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 口試委員會審定書i
致謝ii 中文摘要iii Abstract iv 1 Introduction 1 1.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2 Thirring Model 3 2.1 Spin Representation of the Thirring Model . . . . . . . . . . . . . . . 3 2.2 Chiral Condensate . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.3 Mapping to the Classical 2D XY Model . . . . . . . . . . . . . . . . 5 3 Tensor Network and Matrix Product state 6 3.1 Tensor Network and Tensor Diagram . . . . . . . . . . . . . . . . . . 6 3.2 Matrix Product States . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.3 Uniform Matrix Product States . . . . . . . . . . . . . . . . . . . . . 10 3.4 Expectation Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.5 Gauge Degrees of Freedom, Canonical Form and Symmetric gauge . . 12 3.6 Geometric Series for Transfer Matrix . . . . . . . . . . . . . . . . . . 16 3.7 Matrix Product Operator . . . . . . . . . . . . . . . . . . . . . . . . 18 4 Variational Optimization Method for uniform Matrix Product State 20 4.1 Effective Hamiltonian . . . . . . . . . . . . . . . . . . . . . . . . . . . 20 4.2 VUMPS algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24 5 Time-Dependent Variational Principle Applied to Matrix Product State 27 5.1 Tangent Vector Space . . . . . . . . . . . . . . . . . . . . . . . . . . 27 5.2 Gauge Fixing for Tangent Vector . . . . . . . . . . . . . . . . . . . . 28 5.3 Projection Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 5.4 TDVP algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 6 Result and Conclusion 34 6.1 Ground State of the Thirring Model . . . . . . . . . . . . . . . . . . 34 6.2 TDVP Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 7 Summary 43 Bibliography 44 Appendix More Numerical Results 46 | |
| dc.language.iso | en | |
| dc.subject | 動態相變 | zh_TW |
| dc.subject | 張量網路 | zh_TW |
| dc.subject | 矩陣乘積態 | zh_TW |
| dc.subject | 均勻矩陣乘積態的變分優化演算法 | zh_TW |
| dc.subject | 時間相依變分原理 | zh_TW |
| dc.subject | Tirring 模型 | zh_TW |
| dc.subject | 量子演化 | zh_TW |
| dc.subject | tensor network (TN) | en |
| dc.subject | variational optimization algorithm for uniform matrix product state (VUMPS) | en |
| dc.subject | matrix product state (MPS) | en |
| dc.subject | dynamical phase transition (DPT) | en |
| dc.subject | quantum quench | en |
| dc.subject | Thirring model | en |
| dc.subject | time-dependent variational principle (TDVP) | en |
| dc.title | 張量網路演算法對Thirring 模型在一維無限長格點之研究 | zh_TW |
| dc.title | Tensor Network Studies of Thirring Model on a One-dimensional Infinite-size Lattice | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 林及仁(Chi-Jen David Lin),陳柏中(Po-Chung Chen) | |
| dc.subject.keyword | 張量網路,矩陣乘積態,均勻矩陣乘積態的變分優化演算法,時間相依變分原理,Tirring 模型,量子演化,動態相變, | zh_TW |
| dc.subject.keyword | tensor network (TN),matrix product state (MPS),variational optimization algorithm for uniform matrix product state (VUMPS),time-dependent variational principle (TDVP),Thirring model,quantum quench,dynamical phase transition (DPT), | en |
| dc.relation.page | 53 | |
| dc.identifier.doi | 10.6342/NTU201802766 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2018-08-08 | |
| 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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|---|---|---|---|
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