Non-Hermitian free-fermion critical systems and logarithmic conformal field theory
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| Format: | Preprint |
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2026
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| _version_ | 1866911568272293888 |
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| author | Io, Iao-Fai Huang, Fu-Hsiang Hsieh, Chang-Tse |
| author_facet | Io, Iao-Fai Huang, Fu-Hsiang Hsieh, Chang-Tse |
| contents | Conformal invariance often accompanies criticality in Hermitian systems. However, its fate in non-Hermitian settings is less clear, especially near exceptional points where the Hamiltonian becomes non-diagonalizable. Here we investigate whether a 1+1-dimensional gapless non-Hermitian system can admit a conformal description, focusing on a PT-symmetric free-fermion field theory. Working in the biorthogonal formalism, we identify the conformal structure of this theory by constructing a traceless energy-momentum tensor whose Fourier modes generate a Virasoro algebra with central charge $c=-2$. This yields a non-Hermitian, biorthogonal realization of a logarithmic conformal field theory, in which correlation functions exhibit logarithmic scaling and the spectrum forms Virasoro staggered modules that are characterized by universal indecomposability parameters. We further present a microscopic construction and show how the same conformal data (with finite-size corrections) can be extracted from the lattice model at exceptional-point criticality, thereby supporting the field-theory prediction. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2602_02649 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Non-Hermitian free-fermion critical systems and logarithmic conformal field theory Io, Iao-Fai Huang, Fu-Hsiang Hsieh, Chang-Tse Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Physics Conformal invariance often accompanies criticality in Hermitian systems. However, its fate in non-Hermitian settings is less clear, especially near exceptional points where the Hamiltonian becomes non-diagonalizable. Here we investigate whether a 1+1-dimensional gapless non-Hermitian system can admit a conformal description, focusing on a PT-symmetric free-fermion field theory. Working in the biorthogonal formalism, we identify the conformal structure of this theory by constructing a traceless energy-momentum tensor whose Fourier modes generate a Virasoro algebra with central charge $c=-2$. This yields a non-Hermitian, biorthogonal realization of a logarithmic conformal field theory, in which correlation functions exhibit logarithmic scaling and the spectrum forms Virasoro staggered modules that are characterized by universal indecomposability parameters. We further present a microscopic construction and show how the same conformal data (with finite-size corrections) can be extracted from the lattice model at exceptional-point criticality, thereby supporting the field-theory prediction. |
| title | Non-Hermitian free-fermion critical systems and logarithmic conformal field theory |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Quantum Physics |
| url | https://arxiv.org/abs/2602.02649 |