Motivated by recent advances in fabricating artificial lattices in semiconductors and their promise for quantum simulation of topological materials, we study the one-dimensional dimerized Fermi–Hubbard model. We show how the topological phases at half-filling can be characterized by a reduced Zak phase defined based on the reduced density matrix of each spin subsystem. Signatures of bulk–boundary correspondence are observed in the triplon excitation of the bulk and the edge states of uncoupled spins at the boundaries. At quarter-filling, we show that owing to the presence of the Hubbard interaction the system can undergo a transition to the topological ground state of the non-interacting Su–Schrieffer–Heeger model with the application of a moderate-strength external magnetic field. We propose a robust experimental realization with a chain of dopant atoms in silicon or gate-defined quantum dots in GaAs where the transition can be probed by measuring the tunneling current through the many-body state of the chain.

受半导体中制造人工晶格的最新进展及其对拓扑材料的量子模拟的希望所推动，我们研究了一维二聚费米-哈伯德模型。我们展示了如何根据每个自旋子系统的密度矩阵降低而定义的Zak相减少来表征半填充时的拓扑相。在体的三重激发和边界处未耦合的自旋的边缘状态中观察到体-边界对应的签名。在四分之一填充过程中，我们表明，由于存在哈伯德相互作用，因此在施加中等强度的外部磁场的作用下，系统可能会过渡到非相互作用的Su–Schrieffer–Heeger模型的拓扑基态。