Single-particle Green’s functions and interacting topological insulators

By V. Gurarie. 2010

258 citations recorded by the source corpus.

We study topological insulators characterized by the integer topological invariant Z, in even and odd spacial dimensions. These are well understood in case when there are no interactions. We extend the earlier work on this subject to construct their topological invariants in terms of their Green's functions. In this form, they can be used even if there are interactions. Specializing to one and two spacial dimensions, we further show that if two topologically distinct topological insulators border each other, the difference of their topological invariants is equal to the difference between the number of zero energy boundary excitations and the number of zeroes of the Green's function at the boundary. In the absence of interactions Green's functions have no zeroes thus there are always edge states at the boundary, as is well known. In the presence of interactions, in principle Green's functions could have zeroes. In that case, there could be no edge states at the boundary of two topological insulators with different topological invariants. This may provide an alternative explanation to the recent results on one dimensional interacting topological insulators.

Subfields: Atomic and Molecular Physics, and Optics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/5b514dc3e5ab8210ffd925b630522f9629e486a0

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In Atomic and Molecular Physics, and Optics

In Materials Chemistry

Citations in the corpus

Simplified Topological Invariants for Interacting Insulators (2012, methodology): “[25] V.”
Classification of topological quantum matter with symmetries (2015, methodology): “Topological invariants can also be written in terms of Green’s functions (Gurarie, 2011; Ishikawa and Matsuyama, 1987; Volovik, 2003; Wang et al., 2012; Wang and Zhang, 2012) and by using C∗-algebra (Bellissard et al., 1994; Hastings and Loring, 2011; Loring and Hastings, 2010; Prodan, 2014; Prodan…”
Perspective on topological states of non-Hermitian lattices (2019, methodology): “rvables and could therefore be used as an alternative to the Hamiltonian as the starting point for a topological characterization [121, 122]. This has been particularly useful for interacting systems [123]. In the case of non-Hermitian systems, Ref. [120] focuses on the one-dimensional case where th”
Topological characterization of chiral models through their long time dynamics (2017, background): “Future interesting directions opened by this work include a study of the robustness of our observable against static and temporal disorder [38], the extension of this approach to interacting systems [49, 50], and eventually the extension of this proposal to other topological classes.”