Skip to content
DraconiticResearch
Search Sources API
197,578 studies31 sourcesUpdated 26 min ago
PreprintarXiv licencearXiv

Diagrammatic Monte Carlo for Fermionic Rényi Entanglement Entropy

  • Boyuan Shi
Open at sourcePDFDOICite

Abstract

We develop a direct diagrammatic Monte Carlo method for the second Rényi entropy of inter- acting lattice fermions. Fermionic replica sewing yields a connected-determinant (CDet) expansion, which we sample with many-configuration Markov-chain Monte Carlo. On a 3 \times 3 Hubbard clus- ter, deterministic coefficients through third order agree with exact-diagonalization derivatives for three reference shifts, while sampling extends the series to tenth order. For a reference shift with a continuous stability region, conformal-Borel resummation also gives good agreement with the exact entropy. We further compute coefficients through ninth order on 40 \times 40 and 50 \times 50 periodic lat- tices, with subsystems of up to 676 sites. The resummed results from different reference shifts show good agreement at a common truncation order. Their shift and order dependence provide checks on the stability of the continuation. These calculations extend connected-diagram sampling to spatial Rényi observables on large finite fermionic systems.

Related

  1. New Developments in Diagrammatic Monte Carlo for Interacting Lattice Fermions: Efficient Algorithms and Applications
    Boyuan Shi
    arXivPreprintarXiv licenceFull textComputational physicsCondensed matterarXiv
  2. Vectorized Symmetric and Fermionic Tensor Network Implementations for GPU-Accelerated Variational Monte Carlo
    Si-Jing Du, Johnnie Gray, Ao Chen +1
    arXivPreprintarXiv licenceFull textComputational physicsCondensed matterarXiv
  3. Self-Healing Diffusion Monte Carlo applied to a simple fermionic model: A critical assessment of the method
    Michel Caffarel, Manon Pinar, Anthony Scemama
    HALPreprintCC BY 4.0Full textComputational physicsCondensed matterHALarXiv
  4. Self-assembly Monte Carlo reveals localized entanglement in giant polymer melts
    Enrico Fornasa, Francesco Slongo, Cristian Micheletti
    arXivPreprintCC BY-NC-ND 4.0Full textBiophysicsBiological & medical physicsarXiv
  5. Operator-Space Entanglement Entropy in Random Fermionic Gaussian Dynamics
    Pablo Bayona-Pena, Elena Gramellini, Lorenzo Piroli
    arXivPreprintarXiv licenceFull textMathematical physicsQuantum physics & quantum informationarXiv

Cite

BibTeXRIS
BibTeX
@misc{shi2026diagrammatic,
  title = {{Diagrammatic Monte Carlo for Fermionic Rényi Entanglement Entropy}},
  author = {Boyuan Shi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.21632},
  eprint = {2605.21632},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.21632},
}
RIS
TY  - UNPB
TI  - Diagrammatic Monte Carlo for Fermionic Rényi Entanglement Entropy
AU  - Boyuan Shi
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2605.21632
UR  - https://arxiv.org/abs/2605.21632
AB  - We develop a direct diagrammatic Monte Carlo method for the second Rényi entropy of inter- acting lattice fermions. Fermionic replica sewing yields a connected-determinant (CDet) expansion, which we sample with many-configuration Markov-chain Monte Carlo. On a 3 \times 3 Hubbard clus- ter, deterministic coefficients through third order agree with exact-diagonalization derivatives for three reference shifts, while sampling extends the series to tenth order. For a reference shift with a continuous stability region, conformal-Borel resummation also gives good agreement with the exact entropy. We further compute coefficients through ninth order on 40 \times 40 and 50 \times 50 periodic lat- tices, with subsystems of up to 676 sites. The resummed results from different reference shifts show good agreement at a common truncation order. Their shift and order dependence provide checks on the stability of the continuation. These calculations extend connected-diagram sampling to spatial Rényi observables on large finite fermionic systems.
ER  -