張量網路演算法對Thirring 模型在一維無限長格點之研究

Tensor Network Studies of Thirring Model on a One-dimensional Infinite-size Lattice

洪浩迪(Hao-Ti Hung)

指導教授 ： 高英哲

國立臺灣大學/理學院/物理學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201802766

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

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)

參考文獻

[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.