论文标题
从Ising模型到Kitaev链 - 拓扑相变的简介
From Ising model to Kitaev Chain -- An introduction to topological phase transitions
论文作者
论文摘要
在这篇一般文章中，我们将铁磁性的一维横向场量子量量模型映射到Kitaev的一维P波超导体，该模型在耐断层的拓扑量子计算中应用。将Pauli的横向IS链的旋转操作员映射到逆Jordan-Wigner Transformation的无旋转费用创建和歼灭操作员，导致与Kitaev链紧密相关的Hamiltonian形式，该形式表现出拓扑相过渡，其中相位表现为相位的特征，其特征是不同的拓扑表征，在过渡点上不连续变化。 Kitaev链在非平凡的拓扑阶段支持两个Majorana零模式（MZM），而没有一个零模式。铁磁相中的横向液的双层基态对应于由MZM制成的非本地游离费米度。 Ising链的准粒子激发，即铁磁相中的结构域壁形成，在顺磁相图中与Bogoliubon兴奋中的旋转叶片。该映射表明，可以为基塔耶夫链来定义非本地秩序参数，以与兰道理论的通常范式一起使用。
In this general article, we map the one-dimensional transverse field quantum Ising model of ferromagnetism to Kitaev's one-dimensional p-wave superconductor, which has its application in fault-tolerant topological quantum computing. Mapping Pauli's spin operators of transverse Ising chain to spinless fermionic creation and annihilation operators by Inverse Jordan-Wigner transformation leads to a Hamiltonian form closely related to Kitaev Chain, which exhibits topological phase transition where phases are characterized by different topological invariant that changes discontinuously at the transition point. Kitaev Chain supports two Majorana zero modes (MZMs) in the non-trivial topological phase, while none is in the trivial phase. The doubly degenerate ground state of the transverse Ising in ferromagnetic phase corresponds to non-local free fermion degree made from MZMs. The quasi-particle excitations of Ising chain, viz., domain wall formation in the ferromagnetic phase and spin-flip in paramagnetic phase maps to Bogoliubon excitations. The mapping suggests that a non-local order parameter can be defined for Kitaev Chain to work with the usual paradigm of Landau's theory.
