Current browse context:
cond-mat.str-el
Change to browse by:
References & Citations
Condensed Matter > Strongly Correlated Electrons
Title: Bulk-boundary correspondence and singularity-filling in long-range free-fermion chains
(Submitted on 28 Nov 2022 (v1), last revised 14 Apr 2023 (this version, v3))
Abstract: The bulk-boundary correspondence relates topologically-protected edge modes to bulk topological invariants, and is well-understood for short-range free-fermion chains. Although case studies have considered long-range Hamiltonians whose couplings decay with a power-law exponent $\alpha$, there has been no systematic study for a free-fermion symmetry class. We introduce a technique for solving gapped, translationally invariant models in the 1D BDI and AIII symmetry classes with $\alpha>1$, linking together the quantized winding invariant, bulk topological string-order parameters and a complete solution of the edge modes. The physics of these chains is elucidated by studying a complex function determined by the couplings of the Hamiltonian: in contrast to the short-range case where edge modes are associated to roots of this function, we find that they are now associated to singularities. A remarkable consequence is that the finite-size splitting of the edge modes depends on the topological winding number, which can be used as a probe of the latter. We furthermore generalise these results by (i) identifying a family of BDI chains with $\alpha<1$ where our results still hold, and (ii) showing that gapless symmetry-protected topological chains can have topological invariants and edge modes when $\alpha -1$ exceeds the dynamical critical exponent.
Submission history
From: Nick Jones [view email][v1] Mon, 28 Nov 2022 19:00:02 GMT (609kb,D)
[v2] Tue, 20 Dec 2022 14:46:51 GMT (610kb,D)
[v3] Fri, 14 Apr 2023 12:56:18 GMT (619kb,D)
Link back to: arXiv, form interface, contact.