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.

Enhanced superconductivity and various edge modes in modulated $t$-$J$ chains

“…Here λ is the amplitude of the modulation, p is the size of the unit cell, and φ is the phase factor. These kinds of modulations are very common in researching topological insulators in 1D optical superlattices [17,23,27,39,40].…”

“…The 1D quasi-periodic superlattice has been attracting continuous investigations in the last decade, partially because of its nontrivial topological nature [17][18][19][20][21][22][23]. In a noninteracting setting, the essential physics behind it is well understood, that these 1D quasi-periodic models can be mapped to the 2D Harper-Hofstadter model [24,25] which is used to describe the quantum Hall effect [26].…”

“…In a noninteracting setting, the essential physics behind it is well understood, that these 1D quasi-periodic models can be mapped to the 2D Harper-Hofstadter model [24,25] which is used to describe the quantum Hall effect [26]. In the presence of interactions, there occur more unique phenomena such as fractional topological insulators [19,20] and topological Mott insulators [21][22][23]. Moreover, in the spinful fermionic Hubbard chain, the spin-charge separation due to the confined geometry can also affect topological properties, leading to the phase transition with the low-energy edge excitations change from spin-1/2 fermionic single-particle modes to spin-1 bosonic collective modes at specific fillings [27].…”

Topological phases in the Fermi-Hofstadter-Hubbard model on hybrid-space ladders

“…* heidrich-meisner@uni-goettingen. de In a previous work [20], we showed that Hubbard interactions in a fermionic, one-dimensional charge pump can change its topological properties: Without interactions, the Chern number is C = 2, but strong repulsion changes it to C = −1. Note that we change the sign convention for C relative to [20].…”

Topological magnon insulator and quantized pumps from strongly-interacting bosons in optical superlattices

“…Besides, the interacting fermionic SSH model was shown to exhibit unusual correlation dynamics upon a quench [19], which can be attributed to a rich interplay between the presence of topological edge modes and spin-charge separation in one dimension. Finally, quantized pumps of interacting bosons [20] and fermions [21] were also recently investigated.…”