Scaling laws for non-Hermitian skin effect with long-range couplings

Abstract

Recent years have witnessed a surge of research on the non-Hermitian skin effect (NHSE) in one-dimensional lattices with finite-range couplings. In this work, we show that the long-range couplings that decay as $1/l^{\alpha }$ at distance $l$ can fundamentally modify the behavior of NHSE and the scaling of quantum entanglement in the presence of nonreciprocity. At $\alpha =0$, the nonlocality of couplings gives rise to the scale-free skin modes, whose localization length is proportional to the system size. Increasing the exponent $\alpha$ drives a complex-to-real spectral transition and a crossover from a scale-free to constant localization length. Furthermore, the scaling of nonequilibrium steady-state entanglement entropy exhibits a subextensive law due to the nonlocality and the complex spectrum, in contrast to an area law arising from NHSE. Our results provide a theoretical understanding on the interplay between long-range couplings and non-Hermiticity.

6 pages, 4 figures

References in corpus (19)

• Non-Hermitian Physics
• Topological Origin of Non-Hermitian Skin Effects
• Quantum trajectories and open many-body quantum systems
• Efficient Light Funneling based on the non-Hermitian Skin Effect
• Universal non-Hermitian skin effect in two and higher dimensions
• Observation of Non-Hermitian Skin Effect and Topology in Ultracold Atoms
• Acoustic non-Hermitian skin effect from twisted winding topology
• Entanglement entropy for the long range Ising chain
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Observation of non-Bloch parity-time symmetry and exceptional points
• Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
• Measurement-induced dark state phase transitions in long-ranged fermion systems
• Observation of non-Hermitian topological Anderson insulator in quantum dynamics
• Fate of measurement-induced phase transition in long-range interactions
• Simulating non-Hermitian quasicrystals with single-photon quantum walks
• The Lieb-Robinson light cone for power-law interactions
• A non-Hermitian optical atomic mirror
• Edge states of the long-range Kitaev chain: an analytical study
• Optimal State Transfer and Entanglement Generation in Power-law Interacting Systems

Cited by in corpus (8)

• Emergent strength-dependent scale-free mobility edge in a non-reciprocal long-range Aubry-André-Harper model
• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Photon-mediated dipole-dipole interactions as a resource for quantum science and technology in cold atoms
• Non-Hermitian physics of levitated nanoparticle array
• Entangelment Entropy on Generalized Brillouin Zone
• Anisotropic-scaling localization in higher-dimensional non-Hermitian systems
• Concurrent Skin-scale-free Localization and Criticality under Möbius Boundary Conditions in a Non-Hermitian Ladder
• Scaling of Quantum Geometry Near the Non-Hermitian Topological Phase Transitions