Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings

Abstract

A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of 1D system with a non-trivial band topology. An interplay of disorder and topological ordering in the SSH model is of a great interest owing to experimental advancements in synthesized quantum simulators. In this work, we investigate a special sort of a disorder when inter-cell hopping amplitudes are random. Using a definition for ${\mathbb{Z}}_2$-topological invariant $\nu \in \{0;1\}$ in terms of a non-Hermitian part of the total Hamiltonian, we calculate $⟨\nu ⟩$ averaged by random realizations. This allows to find (i) an analytical form of the critical surface that separates phases of distinct topological orders and (ii) finite size fluctuations of $\nu$ for arbitrary disorder strength. Numerical simulations of the edge modes formation and gap suppression at the transition are provided for finite-size system. In the end, we discuss a band-touching condition derived within the averaged Green function method for a thermodynamic limit.

arXiv comment8 pages, 4 figures. Version accepted in Phys. Rev. A

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