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PreprintCC BY 4.0arXiv

Response theory at low temperature for weakly interacting quantum spin systems

  • Joscha Henheik
  • Marius Lemm
  • Tom Wessel
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Abstract

Recent work by Greenblatt, Lange, Marcelli, and Porta (Commun. Math. Phys. 2024) provides the first rigorous justification of adiabatic theory for interacting quantum systems at positive temperature. Their analysis treats weakly interacting lattice fermions and combines a rigorous Wick rotation with fermionic cluster expansion techniques. Here, we study a class of weakly interacting quantum spin systems and derive response theory at positive temperature, thereby covering non-Fermi systems for the first time. Our proof identifies and exploits the locality property of local indistinguishability as a key ingredient in carrying out low-temperature adiabatic expansions. The fact that these systems satisfy local indistinguishability was recently established jointly with Adhikari (arXiv:2508.15907) using cluster expansion methods together with a probabilistic swapping trick.

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Cite

BibTeXRIS
BibTeX
@misc{henheik2026response,
  title = {{Response theory at low temperature for weakly interacting quantum spin systems}},
  author = {Joscha Henheik and Marius Lemm and Tom Wessel},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25249},
  eprint = {2610.25249},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25249},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Response theory at low temperature for weakly interacting quantum spin systems
AU  - Joscha Henheik
AU  - Marius Lemm
AU  - Tom Wessel
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25249
UR  - https://arxiv.org/abs/2610.25249
AB  - Recent work by Greenblatt, Lange, Marcelli, and Porta (Commun. Math. Phys. 2024) provides the first rigorous justification of adiabatic theory for interacting quantum systems at positive temperature. Their analysis treats weakly interacting lattice fermions and combines a rigorous Wick rotation with fermionic cluster expansion techniques. Here, we study a class of weakly interacting quantum spin systems and derive response theory at positive temperature, thereby covering non-Fermi systems for the first time. Our proof identifies and exploits the locality property of local indistinguishability as a key ingredient in carrying out low-temperature adiabatic expansions. The fact that these systems satisfy local indistinguishability was recently established jointly with Adhikari (arXiv:2508.15907) using cluster expansion methods together with a probabilistic swapping trick.
ER  -