研究生: |
羅珮文 Luo, Pei-Wun |
---|---|
論文名稱: |
三角晶格上的鍵結無序量子海森堡反鐵磁體 Random-exchange quantum Heisenberg antiferromagnets on a triangular lattice |
指導教授: |
江府峻
Jiang, Fu-Jiun |
口試委員: | 江佩勳 陳柏中 |
口試日期: | 2021/07/01 |
學位類別: |
碩士 Master |
系所名稱: |
物理學系 Department of Physics |
論文出版年: | 2021 |
畢業學年度: | 109 |
語文別: | 中文 |
論文頁數: | 29 |
中文關鍵詞: | 淬火無序紊亂 、量子海森堡模型 、幾何阻挫 、張量網路 |
英文關鍵詞: | Quenched disorders, quantum Heisenberg model, geometrical frustration, Tensor Network |
研究方法: | 實驗設計法 |
DOI URL: | http://doi.org/10.6345/NTNU202100666 |
論文種類: | 學術論文 |
相關次數: | 點閱:91 下載:14 |
分享至: |
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報 |
本次研究探討二維三角晶格鍵結無序自旋-1/2反鐵磁海森堡模型,想要瞭解其在幾何阻挫性與鍵結無序紊亂的交互影響下系統基態特性的變化。本論文利用張量網路演算法將量子態與哈密爾頓算符分別以矩陣乘積態與矩陣乘積算符表示,再運用密度矩陣重整化群找出量子系統的基態並計算系統的序參數平方子晶格磁化強度(squared sublattice magnetization) $m_s^2$與三子晶格鐵磁序參數(three-sublattice ferromagnetic order parameter) $m_o$。我們發現序參數對鍵結無序紊亂具有穩健性,推測序參數應該只會在鍵結無序紊亂強度為無窮大時才會消失。未來預計計算更大系統尺寸的基態性質,並進行數據擬合。
This thesis is aimed to study the two-dimensional random-exchange spin-1/2 anti-ferromagnetic Heisenberg model on a triangular lattice. The characteristics of the system under the interactive influence of geometric frustration and bond randomness will be investigated. Using the method of tensor network, the quantum state and the Hamiltonian are expressed as the matrix product state and the matrix product operator, respectively. To numerically solve the problem, the density matrix renormalization group method is employed to optimally find the solutions of the ground state of the quantum system, the squared sublattice magnetization $m_s^2$, and the three-sublattice ferromagnetic order parameter $m_o$. It is shown that the order parameter is robust, and the inferred sequencing parameter should only disappear when the strength of the bond disorder is infinite. In the future, we expect to calculate the ground state properties for larger system sizes and will perform data fitting as well.
[1]M. A. Kastner, R. J. Birgeneau, G. Shirane, and Y. Endoh. Magnetic, transport, and optical properties of monolayer copper oxides. Rev.Mod.Phys., 70:897–928, Jul1998.
[2]Kazunori Takada, Hiroya Sakurai, Eiji TakayamaMuromachi, Fujio Izumi, Ruben A. Dilanian, and Takayoshi Sasaki. Superconductivity in twodimensionalCoO2 layers.Nature, 422(6927):53–55, March 2003.
[3]Jacob C Bridgeman and Christopher T Chubb. Handwaving and interpretive dance: an introductory course on tensor networks. Journal of Physics A : Mathematical and Theoretical, 50(22):223001, May 2017.
[4]Ulrich Schollwöck. The densitymatrix renormalization group in the age of matrixproductstates.AnnalsofPhysics,326(1):96–192,2011. January2011SpecialIssue.
[5]N. D. Mermin and H. Wagner. Absence of ferromagnetism or antiferromagnetismin one or twodimensional isotropic heisenberg models. Phys.Rev.Lett., 17:1133–1136, Nov 1966.
[6]J.G.Bednorz and K.A.Müller. Possible high Tc superconductivity in the ba−la−cu−o system. Zeitschrift für Physik B CondensedMatter, 64(2):189–193, Jun 1986.
[7]P. W. ANDERSON. The resonating valence bond state in la2cuo4 and superconductivity. Science, 235(4793):1196–1198, 1987.
[8]Y. Endoh, K. Yamada, R. J. Birgeneau, D. R. Gabbe, H. P. Jenssen, M. A. Kastner,C. J. Peters, P. J. Picone, T. R. Thurston, J. M. Tranquada, G. Shirane, Y. Hidaka,M. Oda, Y. Enomoto, M. Suzuki, and T. Murakami. Static and dynamic spin correlations in pure and dopedLa2cuo4.PhysicalReviewB, 37(13):7443–7453, May1988.
[9]O. P. Vajk. Quantum impurities in the twodimensional spin onehalf Heisenberg antiferromagnet.Science, 295(5560):1691–1695, March 2002.
[10]Anders W. Sandvik. Classical percolation transition in the diluted twodimensional s=1/2 heisenberg antiferromagnet. Phys.Rev.B, 66:024418, Jul 2002.
[11]Nicolas Laflorencie, Stefan Wessel, Andreas Läuchli, and Heiko Rieger. Randomexchange quantum heisenberg antiferromagnets on a square lattice.Phys.Rev.B,73:060403, Feb 2006.
[12]Steven R. White. Density matrix formulation for quantum renormalization groups. Phys.Rev.Lett., 69:2863–2866, Nov 1992.
[13]Román Orús. A practical introduction to tensor networks: Matrix product states and projected entangled pair states. AnnalsofPhysics, 349:117–158, 2014.
[14]U. Schollwöck. The densitymatrix renormalization group.Rev.Mod.Phys.,77:259–315, Apr 2005.
[15]E.M. Stoudenmire and StevenR. White. Studying twodimensional systems with the density matrix renormalizationgroup. Annual Review of Condensed Matter Physics, 3(1):111–128, 2012.
[16]Matthew Fishman, Steven R. White, and E. Miles Stoudenmire. The ITensor software library for tensor network calculations, 2020.
[17]Ken Watanabe, Hikaru Kawamura, Hiroki Nakano, and Tôru Sakai. Quantum spinliquid behavior in the spin1/2 random heisenberg antiferromagnet on the triangular lattice. Journal of the Physical Society of Japan, 83(3):034714, Mar 2014.
[18]Milan Žukovič, Yusuke Tomita, and Y. Kamiya. Ordering phenomena in a heterostructure of frustrated and unfrustrated triangularlattice ising layers. Phys.Rev.E, 96:012145, Jul 2017.
[19]HanQing Wu, ShouShu Gong, and D. N. Sheng. Randomnessinduced spinliquidlike phase in the spin-1/2J1−J2triangular heisenberg model.Phys.Rev.B,99:085141, Feb 2019.