Persistent Haldane phase in carbon tetris chains

authored by: Anas Abdelwahab, Christoph Karrasch, Roman Rausch
Abstract: We introduce the concept of "tetris chains,"which are linear arrays of four-site molecules that differ by their intermolecular hopping geometry. We investigate the fermionic symmetry-protected topological Haldane phase in these systems using Hubbard-type models. The topological phase diagrams can be understood via different competing limits and mechanisms: strong coupling U≫t, weak coupling U≪t, and the weak intermolecular hopping limit t′≪t. Our particular focus is on two tetris chains that are of experimental relevance. First, we show that a "Y-chain"of coarse-grained nanographene molecules (triangulenes) is robustly in the Haldane phase in the whole t′-U plane due to the cooperative nature of the three limits. Secondly, we study a near-homogeneous "Y′-chain"that is closely related to the electronic model for poly(p-phenylene vinylene). In the latter case, the above mechanisms compete, but the Haldane phase manifests robustly and is stable when long-ranged Pariser-Parr-Popple interactions are added. The site-edged Hubbard ladder can also be viewed as a tetris chain, which gives a very general perspective on the emergence of its fermionic Haldane phase. Our numerical results are obtained by large-scale, SU(2)-symmetric tensor network calculations. We employ the density-matrix-renormalization group as well as the variational uniform matrix-product state (VUMPS) algorithms for finite and infinite systems, respectively. The numerics are supplemented by analytical calculations of the band-structure winding number.
Organisation(s): Institute of Theoretical Physics
External Organisation(s): Technische Universität Braunschweig
Type: Article
Journal: Physical Review B
Volume: 111
No. of pages: 10
ISSN: 2469-9950
Publication date: 13.02.2025
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Electronic, Optical and Magnetic Materials, Condensed Matter Physics
Electronic version(s): https://doi.org/10.1103/PhysRevB.111.075129 (Access: Open)
https://doi.org/10.48550/arXiv.2412.08252 (Access: Open)

BibTeX

@article{00406be4b06e4ee7b0e3e8177aaa803c,
title = "Persistent Haldane phase in carbon tetris chains",
abstract = "We introduce the concept of {"}tetris chains,{"}which are linear arrays of four-site molecules that differ by their intermolecular hopping geometry. We investigate the fermionic symmetry-protected topological Haldane phase in these systems using Hubbard-type models. The topological phase diagrams can be understood via different competing limits and mechanisms: strong coupling U≫t, weak coupling U≪t, and the weak intermolecular hopping limit t′≪t. Our particular focus is on two tetris chains that are of experimental relevance. First, we show that a {"}Y-chain{"}of coarse-grained nanographene molecules (triangulenes) is robustly in the Haldane phase in the whole t′-U plane due to the cooperative nature of the three limits. Secondly, we study a near-homogeneous {"}Y′-chain{"}that is closely related to the electronic model for poly(p-phenylene vinylene). In the latter case, the above mechanisms compete, but the Haldane phase manifests robustly and is stable when long-ranged Pariser-Parr-Popple interactions are added. The site-edged Hubbard ladder can also be viewed as a tetris chain, which gives a very general perspective on the emergence of its fermionic Haldane phase. Our numerical results are obtained by large-scale, SU(2)-symmetric tensor network calculations. We employ the density-matrix-renormalization group as well as the variational uniform matrix-product state (VUMPS) algorithms for finite and infinite systems, respectively. The numerics are supplemented by analytical calculations of the band-structure winding number.",
author = "Anas Abdelwahab and Christoph Karrasch and Roman Rausch",
note = "Publisher Copyright: {\textcopyright} 2025 authors. Published by the American Physical Society.",
year = "2025",
month = feb,
day = "13",
doi = "10.1103/PhysRevB.111.075129",
language = "English",
volume = "111",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Institute of Physics",
number = "7",
}