Symmetry-protected third-order exceptional points in staggered flatband rhombic lattices

Abstract

Higher-order exceptional points (EPs), which appear as multifold degeneracies in the spectra of non-Hermitian systems, are garnering extensive attention in various multidisciplinary fields. However, constructing higher-order EPs still remains a challenge due to the strict requirement of the system symmetries. Here we demonstrate that higher-order EPs can be judiciously fabricated in parity–time ( PT )-symmetric staggered rhombic lattices by introducing not only on-site gain/loss but also non-Hermitian couplings. Zero-energy flatbands persist and symmetry-protected third-order EPs (EP3s) arise in these systems owing to the non-Hermitian chiral/sublattice symmetry, but distinct phase transitions and propagation dynamics occur. Specifically, the EP3 arises at the Brillouin zone (BZ) boundary in the presence of on-site gain/loss. The single-site excitations display an exponential power increase in the PT -broken phase. Meanwhile, a nearly flatband sustains when a small lattice perturbation is applied. For the lattices with non-Hermitian couplings, however, the EP3 appears at the BZ center. Quite remarkably, our analysis unveils a dynamical delocalization-localization transition for the excitation of the dispersive bands and a quartic power increase beyond the EP3. Our scheme provides a new platform toward the investigation of the higher-order EPs and can be further extended to the study of topological phase transitions or nonlinear processes associated with higher-order EPs.

Scaling laws of out-of-time-order correlators in a non-Hermitian kicked rotor model

“…For PT -symmetric systems, the dynamics of OTOCs signals the Yang-Lee edge singularity [28] of phase transition and shows the quantized response to external driven potential [29]. It is now widely accepted that the non-Hermiticity is a fundamental modification to conventional quantum mechanics [30][31][32][33][34][35][36] since many systems, such as optics propagation in the "gain-or-loss" medium [37][38][39], the electronics transport in the dissipative circuit [40][41][42][43], and cold atoms in the tailored magneto-optical trap [44][45][46][47][48], are described by a non-Hermitian theory. The extension of Floquet systems to non-Hermitian regimes uncovers rich understandings of physics [49][50][51][52][53].…”