Exact Skin Critical Phase and Configurable Fractal Wavefunctions via Imaginary Gauge Phase Imprint in Non-Hermitian Lattices

TL;DR

This paper introduces a novel method to engineer exact critical and fractal wavefunctions in non-Hermitian lattices, revealing a new skin critical phase with unique multifractal and topological properties.

Contribution

The authors propose the imaginary gauge phase imprint framework, enabling precise control of wavefunctions and uncovering the skin critical phase with distinctive bulk and boundary behaviors.

Findings

Discovery of the skin critical phase with multifractal eigenstates

Eigenstates accumulate at specific bulk interfaces under periodic boundary conditions

Validation of the method in higher dimensions with configurable fractal and Moire states

Abstract

The generation of complex states like multifractal critical states has been an outstanding challenge in both classical and quantum physics. Here we propose a general framework, termed the imaginary gauge phase imprint, allowing to engineer rigorous wavefunctions in any-dimensional non-Hermitian lattices. Using this method, we uncover a novel phase with exact critical wavefunctions in one (and two) dimension, dubbed the skin critical phase (SCP). Unlike conventional critical phases with overall uniform density distributions and non-Hermitian skin effect with eigenstate accumulation at open boundaries, the SCP is marked by a macroscopically multifractal distribution with all critical eigenstates sharing an identical profile and always accumulating at specific bulk interfaces under periodic boundary condition, which become topology-dependent boundary or interface skin modes under open boundary condition. We also show the ballistic dynamics in the SCP, in contrast to the diffusive behaviour in conventional critical phases. Moreover, we validate our method by imprinting configurable wavefunctions in higher dimensions, including complex fractal states with Sierpinski-carpet and Koch-snowflake profiles in non-fractal lattices and Moire states in non-Moire lattices. Our work not only offers fresh insights into fractal phenomena and critical phases, but also provides a rigorous paradigm for wave manipulations in engineered non-Hermitian systems.