Interacting second-order topological insulators in one-dimensional fermions with correlated hopping

TL;DR

This paper introduces a one-dimensional interacting fermion model with correlated hopping that exhibits a second-order topological insulator phase, characterized by gapped edge states and non-local order, which can be simulated in atomic quantum systems.

Contribution

The authors derive a new Hamiltonian for 1D interacting fermions with correlated hopping that supports a second-order topological phase, revealing novel edge states and phase transitions.

Findings

Identification of a second-order topological insulator phase with gapped edge states

Demonstration that strong interactions lead to a superconducting phase

Potential for experimental realization in atomic quantum simulators

Abstract

Higher-order topological crystalline phases in low-dimensional interacting quantum systems represent a challenging and largely unexplored research topic. Here, we derive a Hamiltonian describing fermions interacting through correlated hopping processes that break chiral invariance, but preserve both inversion and time-reversal symmetries. In this way, we show that our one-dimensional model gives rise to an interacting second-order topological insulating phase that supports gapped edge states. The topological nature of such interacting phase turns out to be revealed by both long-range order of a non-local string correlation function and by even degeneracy of the entanglement spectrum. For strong interactions we instead find that the topological crystalline phase is destroyed and replaced by a singlet superconducting phase. The latter, characterized by local fermionic pairing, turns out to appear both in a homogeneous and in a phase separated form. Relevantly, the derived one-dimensional model and the second-order topological insulator can be explored and investigated in atomic quantum simulators.