Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910433282097152 |
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| author | Zhou, Xin-Chi Wang, Ke |
| author_facet | Zhou, Xin-Chi Wang, Ke |
| contents | The critical point of a topological phase transition is described by a conformal field theory (CFT), where the finite-size corrections to the ground state energy are uniquely related to its central charge. We study the finite-size scaling of the energy of non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry ($\mathcal{PT}$) symmetry. We find that under open boundary condition (OBC), the energy scaling $E(L)\sim c/L$ reveals a negative central charge $c=-2$ at the non-Hermitian critical point, indicative of a non-unitary CFT. Furthermore, we discover a universal scaling function capturing the flow of a system from Dirac CFT with $c=1$ to a non-unitary CFT with $c=-2$. The scaling function demonstrates distinct behaviors at topologically non-trivial and trivial sides of critical points. Notably, within the realm of topological criticality, the scaling function exhibits an universal rise-dip-rise pattern, manifesting a characteristic singularity inherent in the non-Hermitian topological critical points. The analytic expression of the scaling function has been derived and is in good agreement with the numerical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01640 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities Zhou, Xin-Chi Wang, Ke Statistical Mechanics Mesoscale and Nanoscale Physics Quantum Physics The critical point of a topological phase transition is described by a conformal field theory (CFT), where the finite-size corrections to the ground state energy are uniquely related to its central charge. We study the finite-size scaling of the energy of non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry ($\mathcal{PT}$) symmetry. We find that under open boundary condition (OBC), the energy scaling $E(L)\sim c/L$ reveals a negative central charge $c=-2$ at the non-Hermitian critical point, indicative of a non-unitary CFT. Furthermore, we discover a universal scaling function capturing the flow of a system from Dirac CFT with $c=1$ to a non-unitary CFT with $c=-2$. The scaling function demonstrates distinct behaviors at topologically non-trivial and trivial sides of critical points. Notably, within the realm of topological criticality, the scaling function exhibits an universal rise-dip-rise pattern, manifesting a characteristic singularity inherent in the non-Hermitian topological critical points. The analytic expression of the scaling function has been derived and is in good agreement with the numerical results. |
| title | Universal non-Hermitian flow in one-dimensional PT-symmetric quantum criticalities |
| topic | Statistical Mechanics Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2405.01640 |