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

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 Z(2)-topological invariant upsilon is an element of {0; 1} in terms of a non-Hermitian part of the total Hamiltonian, we calculate (upsilon) 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 upsilon 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.

Automated summary

This paper investigates the interplay of disorder and topological ordering in the Su-Schrieffer-Heeger (SSH) model, particularly in the case of random intercell hopping amplitudes. By calculating the average of the Z(2) topological invariant upsilon, based on the non-Hermitian part of the total Hamiltonian, we determine the analytical form of the critical surface and the finite-size fluctuations of upsilon for arbitrary disorder strength. Numerical simulations are used to study the formation of edge modes and the suppression of the energy gap at the transition in finite-size systems. Furthermore, we discuss a band-touching condition derived from the averaged Green's function method for the thermodynamic limit.