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arXiv · 2111.15500

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

D. S. Shapiro·S. V. Remizov·A. V. Lebedev·D. V. Babukhin·R. S. Akzyanov·A. A. Zhukov·L. V. Bork
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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.

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BibTeXRIS

D. S. Shapiro, S. V. Remizov, A. V. Lebedev, D. V. Babukhin, R. S. Akzyanov, A. A. Zhukov, L. V. Bork. 2021-11-30. Critical phase boundary and finite-size fluctuations in Su-Schrieffer-Heeger model with random inter-cell couplings. https://doi.org/10.1103/physreva.105.023321

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