Exact Skin Critical Phase and Configurable Fractal Wavefunctions via Imaginary Gauge Phase Imprint in Non-Hermitian Lattices
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arXiv
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| Natura: | Preprint |
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2026
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| author | Dong, Ji-Long Zhu, Shi-Liang Zhang, Dan-Wei |
| author_facet | Dong, Ji-Long Zhu, Shi-Liang Zhang, Dan-Wei |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28153 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Skin Critical Phase and Configurable Fractal Wavefunctions via Imaginary Gauge Phase Imprint in Non-Hermitian Lattices Dong, Ji-Long Zhu, Shi-Liang Zhang, Dan-Wei Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics Quantum Physics 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. |
| title | Exact Skin Critical Phase and Configurable Fractal Wavefunctions via Imaginary Gauge Phase Imprint in Non-Hermitian Lattices |
| topic | Disordered Systems and Neural Networks Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2603.28153 |