Percolation-induced PT symmetry breaking

Abstract

We propose a new avenue in which percolation, which has been much associated with critical phase transitions, can also dictate the asymptotic dynamics of non-Hermitian systems by breaking PT symmetry. Central to it is our newly-designed mechanism of topologically guided gain, where chiral edge wavepackets in a topological system experience non-Hermitian gain or loss based on how they are topologically steered. For sufficiently wide topological islands, this leads to irreversible growth due to positive feedback from interlayer tunneling. As such, a percolation transition that merges small topological islands into larger ones also drives the edge spectrum across a real to complex transition. Our discovery showcases intriguing dynamical consequences from the triple interplay of chiral topology, directed gain and interlayer tunneling, and suggests new routes for the topology to be harnessed in the control of feedback systems.

5 pages with 3 figures in the main text. 19 pages in the Supplemental Material. Comments are welcome

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• Exact Solutions Disentangle Higher-Order Topology in 2D Non-Hermitian Lattices
• Versatile Control of Nonlinear Topological States in Non-Hermitian Systems
• Intrinsic-perturbation induced anomalous higher-order boundary states in non-Hermitian systems
• Nonlinear Hall effects with an exceptional ring
• Observation of edge solitons and transitions between them in a trimer circuit lattice
• Many-body critical non-Hermitian skin effect
• Non-Hermitian ultra-strong bosonic clustering through interaction-induced caging
• Topologically protected negative entanglement
• Deterministic scale-invariant dynamics in a logistic Game-of-Life model
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Size-Dependent Skin Effect Transitions in Weakly Coupled Non-Reciprocal Chains
• Quantum-to-semiclassical Husimi dynamics of non-Hermitian localization transitions
• Reversing non-Hermitian skin accumulation with a non-local transverse switch