時間演化區塊消除法在二維正方易辛模型上的應用

Plaquette Infinite Time-evolving Block-Decimation Method for the Transverse Ising Model on 2D Square Lattices

王彥植(Yen-Chih Wang)

指導教授 ： 高英哲

國立臺灣大學/理學院/物理研究所/碩士(2013年)

https://doi.org/10.6342/NTU.2013.02010

摘要

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。

關鍵字

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

並列摘要

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.

並列關鍵字

matrix product state ； infinite time-evolving block-decimation (iTEBD) ； plaquette ； tensor renormalization group ； brute-force search

參考文獻

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