论文标题
$ su（q）$量子链和二元方程的拓扑泵
Topological pump of $SU(Q)$ quantum chain and Diophantine equation
论文作者
论文摘要
$ su（q）$量子链的拓扑泵与电流相关联，这是由于本地$ [u（1）]^{\ otimes q} $ coguge gouge formate formions的不变性。 $ su（q）$不变二聚体阶段的特征是$ z_q $贝里阶段作为拓扑订单参数，其$ d $维二二维扭曲空间（$ d = q-1 $）是合成的布里素区域。通过包含由理性参数$φ= p/q $指定的对称性破坏扰动，围在相边界周围的泵的特征是$ q $ chern数字与与统一的无限无限曲折有关的电流相关的泵。对开放/周期/扭曲边界条件下系统的分析阐明了泵的块状对应关系，其中质量中心（COM）产生的大型仪表转换起着核心作用。使用二苯胺方程给出了Chern数字的明确公式。已经提出了通过确切的对角线化和有限系统的DMRG的数值证明（$ Q = 3,4 $和5 $），以确认低能谱，边缘状态，COM，CHERN，CHERN数字和批量边缘的一般讨论。还提到了一般$ su（q）$量子链的修改后的lieb-schultz-mattis类型参数。
A topological pump of the $SU(Q)$ quantum chain is proposed associated with a current due to a local $[U(1)]^{\otimes Q}$ gauge invariance of colored fermions. The $SU(Q)$ invariant dimer phases are characterized by the $Z_Q$ Berry phases as a topological order parameter with a $d$-dimensional twist space ($d=Q-1$) as a synthetic Brillouin zone. By inclusion of the symmetry breaking perturbation specified by a rational parameter $Φ=P/Q$, the pump, that encloses around the phase boundary, is characterized by the $Q$ Chern numbers associated with the currents due to uniform infinitesimal twists. The analysis of the systems under the open/periodic/twisted boundary conditions clarifies the bulk-edge correspondence of the pump where the large gauge transformation generated by the center of mass (CoM) plays a central role. An explicit formula for the Chern number is given by using the Diophanine equation. Numerical demonstration by the exact diagonalization and the DMRG for finite systems ($Q=3,4$ and $5$) have been presented to confirm the general discussions for low energy spectra, edge states, CoM's, Chern numbers and the bulk-edge correspondence. A modified Lieb-Schultz-Mattis type argument for the general $SU(Q)$ quantum chain is also mentioned.
