Kavli Affiliate: Shenghan Jiang
| First 5 Authors: Chao Xu, Yunlong Zang, Yixin Ma, Yingfei Gu, Shenghan Jiang
| Summary:
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.
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