Non-Hermitian Quantum Fractals

Abstract

The first quantum fractal discovered in physics is the Hofstadter butterfly. It stems from large external magnetic fields. We discover instead a new class of non-Hermitian quantum fractals (NHQFs) emerging in coupled Hatano-Nelson models on a tree lattice in absence of any fields. Based on analytic solutions, we are able to rigorously identify the self-similar recursive structures in energy spectrum and wave functions. We prove that the complex spectrum of NHQFs bears a resemblance to the Mandelbrot set in fractal theory. The self-similarity of NHQFs is rooted in the interplay between the iterative lattice configuration and non-Hermiticity. Moreover, we show that NHQFs exist in generalized non-Hermitian systems with iterative lattice structures. Our findings open a new avenue for investigating quantum fractals in non-Hermitian systems.

7 pages, 4 figures

References in corpus (20)

• Anderson Transitions
• Topological Origin of Non-Hermitian Skin Effects
• Edge Modes, Degeneracies, and Topological Numbers in Non-Hermitian Systems
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Observation of hybrid higher-order skin-topological effect in non-Hermitian topolectrical circuits
• Acoustic non-Hermitian skin effect from twisted winding topology
• Inner Skin Effects on Non-Hermitian Topological Fractals
• Higher-order topological phases on fractal lattices
• Enhancement of Second-Order Non-Hermitian Skin Effect by Magnetic Fields
• Universality of Hofstadter butterflies on hyperbolic lattices
• Localization in random fractal lattices
• Higher-order topological phases in crystalline and non-crystalline systems: a review
• Hybrid higher-order skin-topological effect in hyperbolic lattices
• Transition from metal to higher-order topological insulator driven by random flux
• Topological Random Fractals
• Observation of squeezed Chern insulator in an acoustic fractal lattice
• Fractal Nodal Band Structures
• Fractal Surface States in Three-Dimensional Topological Quasicrystals
• Fractal states of the Schwinger model

Cited by in corpus (6)

• Quasiperiodicity-induced bulk localization with self similarity in non-Hermitian systems
• Non-Hermitian Skin Effect Along Hyperbolic Geodesics
• Inner non-Hermitian skin effect on Bethe lattice
• Multifractal statistics of non-Hermitian skin effect on the Cayley tree
• Mobility-edge-embedded Hofstadter butterfly from a tilt-induced quasiperiodic potential
• Topological states and flat bands in exactly solvable decorated Cayley trees