張量網狀態在二維量子自旋系統的應用

Abstract

張量網狀態 (tensor network states)可作為研究量子自旋系統基態的試驗波函數。在這一篇論文裡，我們介紹兩種方法，為張量糾纏重整化群 (tensor entanglement renormalization group)及方磚重整法 (plaquette renormalization scheme)。張量糾纏重整化群使用張量乘積態 (tensor product states)做為試驗波函數且為了有效率的計算做了估計。方磚重整法使用方磚重整態 (plaquette renormalized states)做為試驗波函數而不需要做估計。我們使用二維的伊辛模型 (Ising model)來驗證這些方法我們發現張量糾纏重整化群在相對直接對角化 (exact diagonalization)的大尺寸下可使用。藉由使用方磚重整態，我們能夠有信心地找出量子自旋系統的基態。

Tensor network states can be used as a trial wave function to study ground states for quantum spin systems. In this thesis, we introduce two methods, tensor entanglement renormalization group (TERG) method and plaquette renormalization scheme. TERG uses tensor product states as a trial wave function and does an approximation for efficient calculations. Plaquette renormalization scheme uses plaquette renormalized states as a trial wave function without approximate procedures. We demonstrate these methods with two dimensional transverse Ising model. It’s shown that TERG works in a large size compared to exact diagonalization. By using plaquette renormalized states, we can represent ground states faithfully for frustrated spin systems.