Topological and non-topological features of generalized Su-Schrieffer-Heeger models

Abstract

The (one-dimensional) Su-Schrieffer-Heeger Hamiltonian, augmented by spin-orbit coupling and longer-range hopping, is studied at half filling for an even number of sites. The ground-state phase diagram depends sensitively on the symmetry of the model. Charge-conjugation (particle-hole) symmetry is conserved if hopping is only allowed between the two sublattices of even and odd sites. In this case (of BDI symmetry) we find a variety of topologically non-trivial phases, characterized by different numbers of edge states (or, equivalently, different quantized Zak phases). The transitions between these phases are clearly signalled by the entanglement entropy. Charge-conjugation symmetry is broken if hopping within the sublattices is admitted (driving the system into the AI symmetry class). We study specifically next-nearest-neighbor hopping with amplitudes $t_a$ and $t_b$ for the $A$ and $B$ sublattices, respectively. For $t_a=t_b$ parity is conserved, and also the quantized Zak phases remain unchanged in the gapped regions of the phase diagram. However, metallic patches appear due to the overlap between conduction and valence bands in some regions of parameter space. The case of alternating next-nearest neighbor hopping, $t_a=-t_b$, is also remarkable, as it breaks both charge-conjugation $C$ and parity $P$ but conserves the product $CP$. Both the Zak phase and the entanglement spectrum still provide relevant information, in particular about the broken parity. Thus the Zak phase for small values of $t_a$ measures the disparity between bond strengths on $A$ and $B$ sublattices, in close analogy to the proportionality between the Zak phase and the polarization in the case of the related Aubry-André model.

12 pages, 13 figures, accepted for publication in PRB

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• Topological line in frustrated Toric code models
• Effects of correlations on phase diagrams of the two-dimensional Su-Schrieffer-Heeger model with the longer-range hoppings
• Emergence of Topological Non-Fermi Liquid Phases in a Modified Su-Schrieffer-Heeger Chain with Long-Range Interactions
• Entanglement entropy of XX spin $1/2$ chain with random partitioning at arbitrary temperature
• Frustrated mixed-spin ladders: Evidence for a bond order wave phase between rung-singlet and Haldane phases
• Partially topological phase in a quantum loop gas model with tension and pressure
• Emergent topological phases in an extended Su-Schrieffer-Heeger model with Rashba spin-orbit interaction, higher order hopping and domain wall
• Floquet topological phases with high Chern numbers in a periodically driven extended Su-Schrieffer-Heeger model
• Entanglement entropy as a probe of topological phase transitions