三角晶格上的鍵結無序量子海森堡反鐵磁體
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2021
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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.
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.
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淬火無序紊亂, 量子海森堡模型, 幾何阻挫, 張量網路, Quenched disorders, quantum Heisenberg model, geometrical frustration, Tensor Network