Absence of dissipation-free topological edge states in quadratic open fermions
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912551087898624 |
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| author | Mao, Liang |
| author_facet | Mao, Liang |
| contents | We prove a no-go theorem: generic quadratic open fermionic systems governed by Lindblad master equations do not host dissipation-free topological edge states protected by the dissipation gap. By analogy with topological insulators and superconductors, we map the Lindblad generator to a first-quantized non-Hermitian matrix representation that plays the role of a band Hamiltonian. Edge modes of this matrix with vanishing real part are exactly dissipation-free. We show that this matrix is always adiabatically deformable, through a symmetry-preserving path, to a topologically trivial Hermitian matrix. Hence no symmetry-protected, dissipation-free edge modes exist in quadratic open fermions. Our results apply to generic quadratic fermionic Lindbladians and require only a gapped bulk and a bounded spectrum. They establish a clear boundary for robust topological phenomena in open fermionic systems. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_03821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absence of dissipation-free topological edge states in quadratic open fermions Mao, Liang Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons Quantum Physics We prove a no-go theorem: generic quadratic open fermionic systems governed by Lindblad master equations do not host dissipation-free topological edge states protected by the dissipation gap. By analogy with topological insulators and superconductors, we map the Lindblad generator to a first-quantized non-Hermitian matrix representation that plays the role of a band Hamiltonian. Edge modes of this matrix with vanishing real part are exactly dissipation-free. We show that this matrix is always adiabatically deformable, through a symmetry-preserving path, to a topologically trivial Hermitian matrix. Hence no symmetry-protected, dissipation-free edge modes exist in quadratic open fermions. Our results apply to generic quadratic fermionic Lindbladians and require only a gapped bulk and a bounded spectrum. They establish a clear boundary for robust topological phenomena in open fermionic systems. |
| title | Absence of dissipation-free topological edge states in quadratic open fermions |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2508.03821 |