# Bulk-entanglement-spectrum correspondence in $PT$- and $PC$-symmetric topological insulators

**Authors:** Ryo Takahashi, Tomoki Ozawa  
**arXiv:** [2403.18372](https://arxiv.org/abs/2403.18372)  
**Date:** 2024-03-27  
**Summary page:** https://www.summarizepaper.com/en/paper/2403.18372v1/

## Key points

- Takahashi and Ozawa study bulk-entanglement-spectrum correspondence in topological insulators with $PT$ and/or $PC$ symmetry
- Edge spectrum remains gapped in systems with nontrivial bulk topology, challenging conventional bulk-boundary correspondence
- Authors provide models for each symmetry class up to three dimensions using a $K$-theoretic approach
- Research raises questions about entanglement spectra behavior in fragile and delicate topological insulators under $PT$ and $PC$ symmetry
- Numerical evidence supports bulk-entanglement-spectrum correspondence in fragile insulators, but rigorous derivation is lacking due to challenges posed by varying numbers of occupied states
- Consideration of how inter-particle interactions may affect the gapless nature of entanglement spectra in these systems
- Study sheds light on a new aspect of topological insulators under specific symmetries and provides insights into the complex relationship between bulk topology and entanglement spectra

## Summary

In this study, Takahashi and Ozawa explore the concept of bulk-entanglement-spectrum correspondence in topological insulators with parity-time ($PT$) and/or parity-particle-hole ($PC$) symmetry. They challenge the conventional bulk-boundary correspondence by revealing that in systems with nontrivial bulk topology, the edge spectrum remains gapped. By using a $K$-theoretic approach, the authors provide models for each symmetry class up to three dimensions, demonstrating how nontrivial topology from $PT$ and/or $PC$ symmetry is manifested in these systems. The research also raises questions about the behavior of entanglement spectra in fragile and delicate topological insulators under $PT$ and $PC$ symmetry. While numerical evidence supports the existence of bulk-entanglement-spectrum correspondence in fragile insulators, rigorous derivation is still lacking due to challenges posed by varying numbers of occupied states compared to band occupations in fragile insulators. The authors also consider how inter-particle interactions may affect the gapless nature of entanglement spectra in these systems. Overall, this study sheds light on a new aspect of topological insulators under specific symmetries and provides insights into the complex relationship between bulk topology and entanglement spectra. These findings not only expand our understanding of exotic quantum states but also pave the way for further investigations into their properties and behaviors under different conditions.