Quantum phases and topological properties of interacting fermions in one-dimensional superlattices

Abstract

The realization of artificial gauge fields in ultracold atomic gases has opened up a path towards experimental studies of topological insulators and, as an ultimate goal, topological quantum matter in many-body systems. As an alternative to the direct implementation of two-dimensional lattice Hamiltonians that host the quantum Hall effect and its variants, topological charge-pumping experiments provide an additional avenue towards studying many-body systems. Here, we consider an interacting two-component gas of fermions realizing a family of one-dimensional superlattice Hamiltonians with onsite interactions and a unit cell of three sites, whose groundstates would be visited in an appropriately defined charge pump. First, we investigate the grandcanonical quantum phase diagram of individual Hamiltonians, focusing on insulating phases. For a certain commensurate filling, there is a sequence of phase transitions from a band insulator to other insulating phases (related to the physics of ionic Hubbard models) for some members of the manifold of Hamiltonians. Second, we compute the Chern numbers for the whole manifold in a many-body formulation and show that, related to the aforementioned quantum phase transitions, a topological transition results in a change of the value and sign of the Chern number. We provide both an intuitive and conceptual explanation and argue that these properties could be observed in quantum-gas experiments.

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Cited by in corpus (25)

• Thouless pumping and topology
• Tailoring quantum gases by Floquet engineering
• Nonlinear Thouless pumping: solitons and transport breakdown
• Competition and interplay between topology and quasi-periodic disorder in Thouless pumping of ultracold atoms
• Quantisation and its breakdown in a Hubbard-Thouless pump
• Effect of disorder on topological charge pumping in the Rice-Mele model
• Splitting of topological charge pumping in an interacting two-component fermionic Rice-Mele Hubbard model
• Interactions enable Thouless pumping in a nonsliding lattice
• Finite-temperature topological invariant for interacting systems
• Topological invariants based on generalized position operators and application to the interacting Rice-Mele model
• Simulating bosonic Chern insulators in one-dimensional optical superlattices
• Thouless pumping and trapping of two-component gap solitons
• Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices
• Nonlinear Thouless Pumping of Solitons Across an Impurity
• Topological Mott Insulator with Bosonic Edge Modes in 1D Fermionic Superlattices
• Transport of Vector Solitons in Spin-Dependent Nonlinear Thouless Pumps
• Phase diagram and topology of the XXZ chain with alternating bonds and staggered magnetic field
• Charge and spin gaps of the ionic Hubbard model with density-dependent hopping
• Anomalous bulk-edge correspondence of nonlinear Rice-Mele model
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• Quantized single-particle Thouless pump induced by topology transfer from a Chern insulator at finite temperature