Skip to content
DraconiticResearch
Search Sources API
181,716 studies31 sourcesUpdated 25 min ago
PreprintCC BY 4.0arXiv

𝒫(Φ)2 Theory from many-body quantum Gibbs states

  • Phan ThĂ nh Nam
  • Zhilin Yang
  • Xiangchan Zhu
Open at sourcePDFDOICite

Abstract

We derive the 𝒫(Φ)2 measure on the two-dimensional unit torus as the rigorous limit of many-body quantum Gibbs states. In particular, the quantum model corresponding to the Φ2p2 measure is formulated in the grand-canonical ensemble with a general symmetric p-body interaction potential which is not required to have a factorized form. Unlike in the Φ42 case investigated by Fröhlich--Knowles--Schlein--Sohinger in \cite{FKSS25}, in the treatment of higher-order interactions, Wick renormalization generates a full hierarchy of lower-order interactions which we organize systematically using a graphical formalism. One key ingredient of our analysis is a logarithmic stability estimate for both the nonlocal Hartree functional and the many-body Hamiltonian that is uniform in the interaction range, allowing us to use the positivity of the leading p-body interaction to control all lower-order terms generated by the Wick counterterms.

Related

  1. Near-Optimal Learning of Quantum Many-Body Systems from Gibbs and Thermal Metastable States via the Stationarity Test
    Tai Hsuan Yang
    arXivPreprintarXiv licenceFull textMathematical physicsQuantum physics & quantum informationarXiv
  2. Schur States and Many-Body Quantum Walks on Line Graphs
    Musung Kang
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsQuantum physics & quantum informationarXiv
  3. Nonlocal Cubic Density Gibbs Measures from Bosonic Gibbs States with Three-Body Interactions
    Hao Liang
    arXivPreprintarXiv licenceFull textAnalysis & PDEsMathematical physicsarXiv
  4. Convex-Gaussianity of fermionic Gibbs states in perturbation theory
    Kaifeng Bu, Yuanjie Ren
    arXivPreprintarXiv licenceFull textMathematical physicsCondensed matterarXiv
  5. A Boson-informed neural network for Ground States of Many-Body Schrödinger equations
    Zhizhong Kong, Jerry Zhijian Yang, Cheng Yuan +1
    arXivPreprintarXiv licenceFull textMathematical physicsAtomic, molecular & optical physicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{nam2026𝒫φ2,
  title = {{$\mathcalP(Φ)_2$ Theory from many-body quantum Gibbs states}},
  author = {Phan ThĂ nh Nam and Zhilin Yang and Xiangchan Zhu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.23084},
  eprint = {2607.23084},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.23084},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - 𝒫(Φ)_2 Theory from many-body quantum Gibbs states
AU  - Phan ThĂ nh Nam
AU  - Zhilin Yang
AU  - Xiangchan Zhu
PY  - 2026
DA  - 2026/10/09
PB  - arXiv
DO  - 10.48550/arxiv.2607.23084
UR  - https://arxiv.org/abs/2607.23084
AB  - We derive the 𝒫(Φ)_2 measure on the two-dimensional unit torus as the rigorous limit of many-body quantum Gibbs states. In particular, the quantum model corresponding to the Φ^2p_2 measure is formulated in the grand-canonical ensemble with a general symmetric p-body interaction potential which is not required to have a factorized form. Unlike in the Φ^4_2 case investigated by Fröhlich--Knowles--Schlein--Sohinger in \cite{FKSS25}, in the treatment of higher-order interactions, Wick renormalization generates a full hierarchy of lower-order interactions which we organize systematically using a graphical formalism. One key ingredient of our analysis is a logarithmic stability estimate for both the nonlocal Hartree functional and the many-body Hamiltonian that is uniform in the interaction range, allowing us to use the positivity of the leading p-body interaction to control all lower-order terms generated by the Wick counterterms.
ER  -