Diagnosing 2D symmetry protected topological states via mixed state anomaly
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866918060071321600 |
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| author | Xu, Chao Zang, Yunlong Ma, Yixin Gu, Yingfei Jiang, Shenghan |
| author_facet | Xu, Chao Zang, Yunlong Ma, Yixin Gu, Yingfei Jiang, Shenghan |
| contents | Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture posits that the entanglement spectrum exhibits the same anomaly as the physical edge spectrum, thereby serving as an entanglement-based fingerprint for identifying topological phases. In this work, we extend the entanglement-based diagnostic tools by demonstrating that the edge anomaly is manifested not only in the entanglement spectrum but also in the reduced density matrix itself, a phenomenon we refer to as the mixed state anomaly. Focusing on the two-dimensional $\mathbb{Z}_2$ SPT phase, we show that this anomaly is subtly encoded in symmetry-twisted mixed states, leading to a topological contribution to the disorder parameter beyond the area law, as well as a spontaneous-symmetry-breaking type long-range order when time reversal symmetry is present. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_13096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Diagnosing 2D symmetry protected topological states via mixed state anomaly Xu, Chao Zang, Yunlong Ma, Yixin Gu, Yingfei Jiang, Shenghan Strongly Correlated Electrons Quantum Physics Symmetry-protected topological (SPT) phases are short-range entangled quantum states characterized by anomalous edge behavior, a manifestation of the bulk-boundary correspondence for topological phases. Moreover, the Li-Haldane conjecture posits that the entanglement spectrum exhibits the same anomaly as the physical edge spectrum, thereby serving as an entanglement-based fingerprint for identifying topological phases. In this work, we extend the entanglement-based diagnostic tools by demonstrating that the edge anomaly is manifested not only in the entanglement spectrum but also in the reduced density matrix itself, a phenomenon we refer to as the mixed state anomaly. Focusing on the two-dimensional $\mathbb{Z}_2$ SPT phase, we show that this anomaly is subtly encoded in symmetry-twisted mixed states, leading to a topological contribution to the disorder parameter beyond the area law, as well as a spontaneous-symmetry-breaking type long-range order when time reversal symmetry is present. |
| title | Diagnosing 2D symmetry protected topological states via mixed state anomaly |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2506.13096 |