Abstract
The extended Hubbard model with an attractive density–density interaction, positive pair hopping, or both, is shown to host topological phases, with a doubly degenerate entanglement spectrum and interacting edge spins. This constitutes a novel instance of topological order which emerges from interactions. When the interaction terms combine in a charge-SU(2) symmetric fashion, a novel partially polarized pseudospin phase appears, in which the topological features of the spin degrees of freedom coexist with long-range η-wave superconductivity. Thus, our system provides an example of an interplay between spontaneous symmetry breaking and symmetry-protected topological order that leads to novel and unexpected properties.
Highlights
Spontaneous symmetry breaking and symmetry-protected topological order (SPTO) constitute two major schemes by which phases of matter can be classified
We report the existence of novel topological phases of the spin degrees of freedom in the 1D Hubbard chain extended by an attractive density–density coupling and a pair hopping with an overall positive coupling constant, which are not dimerized and exhibit notable differences from the Haldane phase, as will be explained below
We have shown that the Hubbard chain with attractive density–density interaction and/or positive pair-hopping hosts topological phases for the spin degrees of freedom which can coexist with various orders in the charge sector, in particular with long-range η-wave superconductivity
Summary
Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Keywords: Hubbard model, topological order, density-matrix renormalization group
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