A Framework for Predicting Entanglement Spectra of Gapless Symmetry-Protected Topological States in One Dimension

Quantum Physics [Submitted on 11 Apr 2026] A Framework for Predicting Entanglement Spectra of Gapless Symmetry-Protected Topological States in One Dimension Wen-Tao Xu, Frank Pollmann, Michael Knap The concept of gapped symmetry-protected topological (SPT) states has been generalized to gapless SPT (gSPT) states. Similar to gapped SPT states, gSPT states in one dimension exhibit universal degeneracies in their entanglement spectra. The entanglement spectra of gSPT states are further described by boundary conformal field theories, whose systematic prediction is a key open question. To address this problem, we focus on the class of gSPT states that are obtained by applying unitary SPT entanglers to trivial, critical states in one dimension. We find that the reduced density matrix of a non-trivial gSPT state can be obtained, either exactly or approximately, by applying a quantum channel to the reduced density matrix of the trivial gSPT state. This quantum channel acts only near the entanglement cut and modifies its corresponding conformal boundary condition, allowing us in turn to predict the boundary conformal field theory describing the entanglement spectra. We apply this framework to gSPT states protected by various symmetries and having different central charges, and further analyze the stability of boundary conditions of the entanglement cut. Our work thereby provides a framework for systematically analyzing and understanding the entanglement spectra of gSPT states. Comments: Main text contains 12 pages, and 10 figures Subjects: Quantum Physics (quant-ph); Statistical Mechanics (cond-mat.stat-mech); Strongly Correlated Electrons (cond-mat.str-el) Cite as: arXiv:2604.10128 [quant-ph]   (or arXiv:2604.10128v1 [quant-ph] for this version)   https://doi.org/10.48550/arXiv.2604.10128 Focus to learn more Submission history From: Wen-Tao Xu [view email] [v1] Sat, 11 Apr 2026 09:48:56 UTC (669 KB) Access Paper: HTML (experimental) view license Current browse context: quant-ph < prev   |   next > new | recent | 2026-04 Change to browse by: cond-mat cond-mat.stat-mech cond-mat.str-el References & Citations INSPIRE HEP NASA ADS Google Scholar Semantic Scholar Export BibTeX Citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer (What is the Explorer?) Connected Papers Toggle Connected Papers (What is Connected Papers?) Litmaps Toggle Litmaps (What is Litmaps?) scite.ai Toggle scite Smart Citations (What are Smart Citations?) Code, Data, Media Demos Related Papers About arXivLabs Which authors of this paper are endorsers? | Disable MathJax (What is MathJax?)