Entanglement signatures of quantum criticality in Floquet non-Hermitian topological systems

TL;DR

Problem: understanding quantum criticality and topological transitions in Floquet non-Hermitian 1D systems. Approach: analyze entanglement entropy and entanglement spectrum of the Floquet SSH model across zero-, $\pi$-, and coexistence-edge regimes; extract universal data from finite-size scaling, confirming $S_A(N)=\frac{c}{3}\ln N + a$ with $c=1$. Key findings: entanglement spectrum shows edge-mode degeneracies and coupling-induced gaps in the coexistence phase; entanglement entropy peaks sharply at transitions and scales logarithmically with $N$, yielding $c=1$; robustness of these indicators persists under $\gamma$ and $t_3$, though phase boundaries shift due to NHSE. Significance: provides a universal entanglement-based diagnostic for Floquet non-Hermitian topological transitions and suggests avenues for exploring generalized Brillouin-zone physics in driven open systems.

Abstract

The entanglement entropy can be an effective diagnostic tool for probing topological phase transitions. In one-dimensional single particle systems, the periodic driving generates a variety of topological phases and edge modes. In this work, we investigate the topological phase transition of the one-dimensional Floquet Su-Schrieffer-Heeger model using entanglement entropy, and construct the phase diagram based on entanglement entropy. The entanglement entropy exhibits pronounced peaks and follows the logarithmic scaling law at the phase transition points, from which we extract the central charge $c=1$. We further investigate the entanglement spectrum to accurately distinguish the different topological phases. In addition, the coupling between zero and $π$ modes leads to characteristic splittings in the entanglement spectrum, signaling their hybridization under periodic driving. These results remain robust in non-Hermitian regimes and in the presence of next-nearest-neighbor hopping, demonstrating the reliability and universality of entanglement entropy as a diagnostic for topological phase transitions.

Figures (5)

• Figure 1: (a) Phase diagram of entanglement entropy in the $T-t_1$ plane, the colorbar represents the magnitude of the entanglement entropy. (b) and (c) The entanglement spectrum $\xi$ and entanglement entropy $S$ as functions of the $t_1$. The black pentagram and red dashed lines correspond to the emergence of topological $\pi$ modes, whereas the black triangle and blue dashed lines correspond to the disappearance of topological zero modes. The parameters are set as follows: $t_2=1$, $\lambda=0.8$, and $N=60$.
• Figure 2: (a) The entanglement spectrum $\xi$ as a function of $t_1$. (b) The entanglement entropy $S$ as a function of $t_1$. In (a) and (b), curves with the same color correspond to the same driving frequency $\omega$. (c) The gap in the entanglement spectrum as a function of the $\omega$ at $t_1=0.8$ in the coexistence phase of topological zero and $\pi$ modes. (d) The entanglement entropy $S$ as a function of $\omega$ at $t_1=0.8$. Other parameters used in the calculations are set as follows: $t_2=1$, $\lambda=0.8$, and $N=60$.
• Figure 3: (a) and (b) The entanglement spectrum $\xi$ as a function of $t_1$, shown near the transition points of the topological $\pi$ mode and zero mode, respectively. (c) and (d) Entanglement entropy as a function of $t_1$ in the vicinity of the phase transition points associated with the $\pi$ mode and the zero mode, respectively. (e) and (f) The logarithmic scaling of entanglement entropy with the total lattice size $N$ at the transition points of the topological zero and $\pi$ modes, respectively. The inserts show the finite-size scaling of $t_{1,m}$ at the maximum of the entanglement entropy $S_{\pi}$ and $S_0$, respectively. Other parameters are set as follows: $t_2=1$, $\lambda=0.8$, and $\omega=3.2$.
• Figure 4: (a) The entanglement entropy phase diagram of the non-Hermitian system in $T-t_1$ plane with $\gamma=0.1$ and $N=60$. (b) and (c) The logarithmic scaling of entanglement entropy with the total lattice size $N$ at the transition points of the topological zero and $\pi$ modes, respectively. The inserts show the finite-size scaling of $t_1$ at the maximum of the entanglement entropy $S_{\pi}$ and $S_0$, respectively. Other parameters used in the calculations are set as follows: $t_2=1$, $t_3=0$, $\lambda=0.8$, $\omega=3.2$, and $\gamma=0.1$.
• Figure 5: (a) The entanglement entropy $S$ as a function of the $t_1$. (b) and (c) The logarithmic scaling of entanglement entropy with the total lattice size $N$ at the transition points of the topological zero and $\pi$ modes, respectively. The inserts show the finite-size scaling of $t_{1,m}$ at the maximum of the entanglement entropy $S_{\pi}$ and $S_0$, respectively. Other parameters used in the calculations are set as follows: $t_2=1$, $t_3=0.15$, $\lambda=0.8$, $\omega=3.2$, and $\gamma=0.1$.