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

Physical Review A: Atomic, Molecular, and Optical physics. 2022. Vol. 105. No. 2. Article 023321.

Dmitriy S. Shapiro, Sergey V. Remizov, Lebedev A., Babukhin D., Akzyanov R.

A dimerized fermion chain, described by Su-Schrieffer-Heeger (SSH) model, is a well-known example of a one-dimensional system with a nontrivial band topology. An interplay of disorder and topological ordering in the SSH model is of great interest owing to experimental advancements in synthesized quantum simulators. In this paper, we investigate a special sort of a disorder when intercell hopping amplitudes are random. Using a definition for Z2-topological invariant ν∈{0;1} in terms of a non-Hermitian part of the total Hamiltonian, we calculate ⟨ν⟩ 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 ν for arbitrary disorder strength. Numerical simulations of the edge modes formation and gap suppression at the transition are provided for the finite-size system. In the end, we discuss a band-touching condition derived within the averaged Green's function method for a thermodynamic limit.

Keywords: Green function, Phase diagrams, quantum phase transitions, topological phases, disordered systems, topological defects, Topological materials