# Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk

Henheik SJ, Teufel S. 2022. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk. Forum of Mathematics, Sigma. 10, e4.

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*Journal Article*|

*Published*|

*English*

Author

Henheik, Sven Joscha

^{ISTA}^{}; Teufel, StefanDepartment

Abstract

We prove a generalised super-adiabatic theorem for extended fermionic systems assuming a spectral gap only in the bulk. More precisely, we assume that the infinite system has a unique ground state and that the corresponding Gelfand–Naimark–Segal Hamiltonian has a spectral gap above its eigenvalue zero. Moreover, we show that a similar adiabatic theorem also holds in the bulk of finite systems up to errors that vanish faster than any inverse power of the system size, although the corresponding finite-volume Hamiltonians need not have a spectral gap.

Keywords

Publishing Year

Date Published

2022-01-18

Journal Title

Forum of Mathematics, Sigma

Acknowledgement

J.H. acknowledges partial financial support by the ERC Advanced Grant ‘RMTBeyond’ No. 101020331. Support for publication costs from the Deutsche Forschungsgemeinschaft and the Open Access Publishing Fund of the University of Tübingen is gratefully acknowledged.

Volume

10

Article Number

e4

eISSN

IST-REx-ID

### Cite this

Henheik SJ, Teufel S. Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk.

*Forum of Mathematics, Sigma*. 2022;10. doi:10.1017/fms.2021.80Henheik, S. J., & Teufel, S. (2022). Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk.

*Forum of Mathematics, Sigma*. Cambridge University Press. https://doi.org/10.1017/fms.2021.80Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.”

*Forum of Mathematics, Sigma*. Cambridge University Press, 2022. https://doi.org/10.1017/fms.2021.80.S. J. Henheik and S. Teufel, “Adiabatic theorem in the thermodynamic limit: Systems with a gap in the bulk,”

*Forum of Mathematics, Sigma*, vol. 10. Cambridge University Press, 2022.Henheik, Sven Joscha, and Stefan Teufel. “Adiabatic Theorem in the Thermodynamic Limit: Systems with a Gap in the Bulk.”

*Forum of Mathematics, Sigma*, vol. 10, e4, Cambridge University Press, 2022, doi:10.1017/fms.2021.80.**All files available under the following license(s):**

**Creative Commons Attribution 4.0 International Public License (CC-BY 4.0):**

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2022-01-19

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### Sources

arXiv 2012.15239