Emergent topological re-entrant phase transition in a generalized quasiperiodic modulated Su-Schrieffer-Heeger model

TL;DR

This work investigates emergent topological re-entrant phase transitions in a generalized quasiperiodic SSH model. By introducing a quasiperiodic modulation of the intracell hopping with tunable boundedness, the authors identify two distinct REPT classes: TI→TAI in the bounded case and TAI→TAI in the unbounded case. The conclusions are supported by real-space winding numbers, bulk-gap analysis, Lyapunov exponents, and zero-mode spectra, and the results suggest possible experimental realization in Rydberg, cold-atom, and photonic systems. Overall, the paper advances understanding of disorder-induced topology in 1D systems and highlights how modulation structure controls REPT behavior.

Abstract

We study the topological properties of the one-dimensional generalized quasiperiodic modulated Su-Schrieffer-Heeger model. The results reveal that topological re-entrant phase transition emerges. Through the analysis of a real-space winding number , we divide the emergent topological re-entrant phase transitions into two types. The first is the re-entrant phase transition from the traditional topological insulator phase into the topological Anderson insulator phase, and the second is the re-entrant phenomenon from one topological Anderson insulator phase into another topological Anderson insulator phase. These two types of re-entrant phase transition correspond to bounded and unbounded cases of quasiperiodic modulation, respectively. Furthermore, we verify the above topological re-entrant phase transitions by analyzing the Lyapunov exponent and bulk gap. Since Su-Schrieffer-Heeger models have been realized in various artificial systems (such as cold atoms, optical waveguide arrays, ion traps, Rydberg atom arrays, etc.), the two types of topological re-entrant phase transition predicted in this paper are expected to be realized in the near future.

Figures (9)

• Figure 1: Schematic diagram of quasiperiodic induced traditional topological phase transitions and topological REPT.
• Figure 2: (a) The real-space winding number $\nu$ as functions of $\lambda$ and $t_{1}$. The red dashed line corresponds to the line of $t_1=0.8$. (b) The bulk gap $(\Delta E)$ as functions of $\lambda$ and $t_1$. (c) The winding number (red solid line) and Lyapunov exponent (black solid line) versus quasiperiodic strength $\lambda$ with $t_1 = 0.8$. (d) The middle $200$ eigenenergies versus $\lambda$ with $t_1 = 0.8$. The emergence of topological zero modes are marked with red lines. Throughout, $b=0.9$.
• Figure 3: Density distribution of the $N$-th and $N+1$-th eigenstates under the condition of $\lambda=0,~0.5,~2,~2.5$ (marked by green squares in Fig. \ref{['2']}). Throughout, we set $t_1=0.8$.
• Figure 4: (a) The real-space winding number $\nu$ as functions of $\lambda$ and $t_{1}$. The red dashed line corresponds to the line of $t_1=1.2$. (b) The bulk gap $(\Delta E)$ as functions of $\lambda$ and $t_1$. (c) The winding number (red solid line) and Lyapunov exponent (black solid line) versus quasiperiodic strength $\lambda$ with $t_1 = 1.2$. (d) The middle $200$ eigenenergies versus $\lambda$ with $t_1 = 1.2$. The emergence of topological zero modes are marked with red lines. Throughout, $b=1.5$.
• Figure 5: Density distribution of the $N$-th and $N+1$-th eigenstates under the condition of $\lambda=0,~0.5,~1.5,~3,~3.5$ (marked by green squares in Fig. \ref{['4']}). Throughout, we set $t_1=1.2$.