Strong and almost strong modes of Floquet spin chains in Krylov subspaces
Strong and almost strong modes of Floquet spin chains in Krylov subspaces
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Krylov 子空间中 Floquet 自旋链的强模式和几乎强模式
DOI：
10.1103/physrevb.104.195121
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发表时间：
2021
影响因子：
3.7
通讯作者：
A. Mitra
中科院分区：
文献类型：
--
作者：
Daniel J. Yates;A. Mitra
已知可积Floquet自旋链具有强零模和π模，它们是分别与Floquet么正交换和反交换的边界算子，除了与Floquet么正的离散对称性反交换之外，还产生频闪时间演化。因此，强模的存在意味着全谱的特征配对结构。弱相互作用将强模修改为几乎与Floquet幺正对易或反对易的几乎强模。给出了强模和几乎强模在两种不同Krylov子空间中的表现形式。一个是从Lanczos迭代得到的Krylov子空间，该子空间将Floquet哈密顿量生成的时间演化映射到具有最近邻跳跃的虚构链上的单个粒子的动力学上。第二个是从Arnoldi迭代得到的Krylov子空间，该子空间将Floquet幺正直接生成的时间演化映射到具有较长范围跳跃的虚构链上的单个粒子的动力学上。前者的Krylov子空间对Floquet么正对数的分支敏感，而后者则不敏感.讨论了Krylov子空间中的有效单粒子模型，着重讨论了Krylov链的拓扑性质，这些性质保证了边界处0和π模的稳定性.相互作用的作用进行了讨论。几乎强模的寿命表达式导出的Krylov子空间的参数，并与精确对角化。
Integrable Floquet spin chains are known to host strong zero and π modes which are boundary operators that respectively commute and anticommute with the Floquet unitary generating stroboscopic time-evolution, in addition to anticommuting with a discrete symmetry of the Floquet unitary. Thus the existence of strong modes imply a characteristic pairing structure of the full spectrum. Weak interactions modify the strong modes to almost strong modes that almost commute or anticommute with the Floquet unitary. Manifestations of strong and almost strong modes are presented in two different Krylov subspaces. One is a Krylov subspace obtained from a Lanczos iteration that maps the time-evolution generated by the Floquet Hamiltonian onto dynamics of a single particle on a fictitious chain with nearest neighbor hopping. The second is a Krylov subspace obtained from the Arnoldi iteration that maps the time-evolution generated directly by the Floquet unitary onto dynamics of a single particle on a fictitious chain with longer range hopping. While the former Krylov subspace is sensitive to the branch of the logarithm of the Floquet unitary, the latter obtained from the Arnoldi scheme is not. The effective single particle models in the Krylov subspace are discussed, and the topological properties of the Krylov chain that ensure stable 0 and π modes at the boundaries are highlighted. The role of interactions is discussed. Expressions for the lifetime of the almost strong modes are derived in terms of the parameters of the Krylov subspace, and are compared with exact diagonalization.
影响因子：
2.9
作者：
Bastidas, V. M.;Emary, C.;Brandes, T.
通讯作者：
Brandes, T.
DOI：
10.1088/1742-5468/aa73f0
发表时间：
2017-06-01
影响因子：
2.4
作者：
Kemp, Jack;Yao, Norman Y.;Fendley, Paul
通讯作者：
Fendley, Paul