Spurious Strange Correlators in Symmetry-Protected Topological Phases
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911627466506240 |
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| author | Gao, Wei-Liang Zhang, Jie-Yu Liu, Zheng-Xin Ye, Peng |
| author_facet | Gao, Wei-Liang Zhang, Jie-Yu Liu, Zheng-Xin Ye, Peng |
| contents | Strange correlator is a powerful tool widely used in detecting symmetry-protected topological (SPT) phases. However, the result of strange correlator crucially relies on the adoption of the reference state. In this work, we report that an ill-chosen reference state can induce spurious long-range strange correlators in trivial SPT phases, leading to false positives in SPT diagnosis. Focusing on 1D gapped bosonic/spin systems described by matrix product states (MPS), we trace the origin of these spurious signals in trivial SPT phases to the magnitude-degeneracy of the transfer matrix. We systematically classify three distinct mechanisms responsible for such degeneracy, each substantiated by concrete examples: (1) the presence of high-dimensional irreducible representations (abbreviated as \emph{irrep}) in the eigenspace corresponding to the entanglment spectrum (entanglement space); (2) a phase mismatch in symmetry representations between the target and reference states; and (3) long-range order arising from symmetry breaking. Our findings clarify the importance of the choice of proper reference states, providing a guideline to avoid pitfalls and correctly identify SPT order using strange correlators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06691 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Spurious Strange Correlators in Symmetry-Protected Topological Phases Gao, Wei-Liang Zhang, Jie-Yu Liu, Zheng-Xin Ye, Peng Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Physics Strange correlator is a powerful tool widely used in detecting symmetry-protected topological (SPT) phases. However, the result of strange correlator crucially relies on the adoption of the reference state. In this work, we report that an ill-chosen reference state can induce spurious long-range strange correlators in trivial SPT phases, leading to false positives in SPT diagnosis. Focusing on 1D gapped bosonic/spin systems described by matrix product states (MPS), we trace the origin of these spurious signals in trivial SPT phases to the magnitude-degeneracy of the transfer matrix. We systematically classify three distinct mechanisms responsible for such degeneracy, each substantiated by concrete examples: (1) the presence of high-dimensional irreducible representations (abbreviated as \emph{irrep}) in the eigenspace corresponding to the entanglment spectrum (entanglement space); (2) a phase mismatch in symmetry representations between the target and reference states; and (3) long-range order arising from symmetry breaking. Our findings clarify the importance of the choice of proper reference states, providing a guideline to avoid pitfalls and correctly identify SPT order using strange correlators. |
| title | Spurious Strange Correlators in Symmetry-Protected Topological Phases |
| topic | Strongly Correlated Electrons Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2512.06691 |