Generalized real-space Chern number formula and entanglement Hamiltonian
- Creators
- Fan, Ruihua
- Zhang, Pengfei
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Gu, Yingfei
Abstract
We generalize a real-space Chern number formula for gapped free fermions to higher orders. Using the generalized formula, we prove recent proposals for extracting thermal and electric Hall conductance from the ground state via the entanglement Hamiltonian in the special case of non-interacting fermions, providing a concrete example of the connection between entanglement and topology in quantum phases of matter.
Copyright and License
© 2023 R. Fan et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.
Acknowledgement
We thank Yiming Chen, Meng Cheng, Daniel Jafferis, Chao-Ming Jian, Charlie Kane, Anton Kapustin, Daniel Parker, Shinsei Ryu, Wanchun Shen, Nikita Sopenko, Ashvin Vishwanath, Huajia Wang and Edward Witten for helpful discussions. We are especially grateful to Alexei Kitaev, whose advice is indispensable for Appendix B.
Funding
RF is supported by NSF-DMR 2220703 (AV). PZ acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech. YG is partly supported by the Simons Foundation through the "It from Qubit" program.
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Additional details
- National Science Foundation
- DMR-2220703
- Simons Foundation
- Walter Burke Institute for Theoretical Physics
- Caltech groups
- Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics