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

TL;DR

This paper analyzes how random inter-cell couplings affect the topological phases of the SSH model, deriving critical boundaries and fluctuations, with numerical and analytical methods, relevant for quantum simulators.

Contribution

It introduces an analytical expression for the critical phase boundary and finite-size fluctuations in the disordered SSH model using a novel topological invariant.

Findings

Derived the critical surface separating topological phases.

Calculated finite-size fluctuations of the topological invariant.

Numerical simulations confirm edge mode behavior at transition.

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 $\langle\nu\rangle$ 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.