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arXiv 2009.04149cond-mat.quant-gas
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一维耦合晶格系统间拓扑转移诱导的量子输运

Quantized transport induced by topology transfer between coupled one-dimensional lattice systems

Lukas Wawer, Rui Li, Michael Fleischhauer

发表信息：
Phys. Rev. A 104, 012209 (2021)
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摘要：

我们表明，拓扑泵在一维（1D）绝缘体可以诱导严格量子化的运输在一个辅助链的非相互作用的费米子弱耦合到第一。输运电荷由绝缘体的虚构哈密顿量的整数拓扑不变量决定，由单粒子关联的协方差矩阵给出。如果原始系统由非相互作用的费米子组成，则该数与原始系统的TKNN（Thouless、Kohmoto、Nightinghale、den Nijs）不变量相同，因此耦合会导致拓扑向辅助链的转移。当扩展到粒子的相互作用，其中TKNN数不存在，在辅助链中的传输电荷定义了一个拓扑不变量的相互作用系统。在某些情况下，这个不变量与牛，无尾和吴（NTW）介绍的TKNN数的多体推广一致。我们说明了非相互作用费米子的Rice-Mele模型在半填充时和扩展超晶格玻色-哈伯德模型在四分之一填充时的拓扑转移到辅助系统。在后一种情况下，感应电荷泵是分数的。

英文摘要：

We show that a topological pump in a one-dimensional (1D) insulator can induce a strictly quantized transport in an auxiliary chain of non-interacting fermions weakly coupled to the first. The transported charge is determined by an integer topological invariant of the ficticious Hamiltonian of the insulator, given by the covariance matrix of single-particle correlations. If the original system consists of non-interacting fermions, this number is identical to the TKNN (Thouless, Kohmoto, Nightinghale, den Nijs) invariant of the original system and thus the coupling induces a transfer of topology to the auxiliary chain. When extended to particles with interactions, for which the TKNN number does not exist, the transported charge in the auxiliary chain defines a topological invariant for the interacting system. In certain cases this invariant agrees with the many-body generalization of the TKNN number introduced by Niu, Thouless, and Wu (NTW). We illustrate the topology transfer to the auxiliary system for the Rice-Mele model of non-interacting fermions at half filling and the extended superlattice Bose-Hubbard model at quarter filling. In the latter case the induced charge pump is fractional.

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