變分張量網路研究用於磁場下之各向異性 Kitaev 模型

Abstract

可解的Kitaev模型為已知的拓撲量子自旋液體，即在其基態具有長程量子糾纏和分數激發態的特性。在各向同性的極限下，模型的激發態為具能隙的阿貝爾流和無隙線性色散的馬約拉納費米子。當於外加磁場下時，磁場導致的量子相變產生，並在非各向同性的效果下產生有趣和尚待釐清的量子相結構。在本工作中，我們使用無限投影糾纏對態(iPEPS)來研究熱力學極限下之反鐵磁性Kitaev模型，我們構造無約束的和對稱性約束的無限投影糾纏對態作為變分擬設，使用角轉移矩陣重整群（CTMRG）演算法來進行物理量測量，並以自動微分技術來最小化能量以優化參數。在對稱性的投影糾纏單體態中，虛擬自由度中對於規範以及局部對稱性的分解是直接的，而不需要透過任何規範鎖定步驟，這讓我們可以利用轉移矩陣光譜和低能量激發態的關聯來研究不同任意子激發的動力學。

The exactly solvable paradigmatic model introduced by Kitaev is known to be a topologically non-trivial Quantum spin liquid (QSL) that exhibits long-range entanglement in the ground states and the fractionalized excitations. In the isotropic limit, the excitations are gapped abelian fluxes and gapless linearly dispersing Majorana fermions. Upon applying the magnetic field, the magnetic-field-induced quantum phase transition occurred, together with the effect of the anisotropy, resulting in an intriguing and uncertain quantum phase structure. In this work, we study the antiferromagnetic Kitaev model in the thermodynamic limit using the infinite projected entangled-pair states (iPEPS), we constructed the unconstrained and symmetric iPEPS as the variational ansatz, we used the Corner Transfer Matrix Renormalization Group (CTMRG) algorithm to do the physical measurement, and perform the optimization by the energy minimization using Automatic differentiation (AD) technique. In the symmetric iPEPS, a decomposition of the the virtual degrees of freedom into gauge and local symmetries is readily available without any gauge fixing procedure, allowing us to investigate the anyon dynamics using the correspondence between the transfer matrix spectrum and low-lying excitations.