---
_id: '13966'
abstract:
- lang: eng
text: We present a low-scaling diagrammatic Monte Carlo approach to molecular correlation
energies. Using combinatorial graph theory to encode many-body Hugenholtz diagrams,
we sample the Møller-Plesset (MPn) perturbation series, obtaining accurate correlation
energies up to n=5, with quadratic scaling in the number of basis functions. Our
technique reduces the computational complexity of the molecular many-fermion correlation
problem, opening up the possibility of low-scaling, accurate stochastic computations
for a wide class of many-body systems described by Hugenholtz diagrams.
acknowledgement: We acknowledge stimulating discussions with Sergey Varganov, Artur
Izmaylov, Jacek Kłos, Piotr Żuchowski, Dominika Zgid, Nikolay Prokof'ev, Boris Svistunov,
Robert Parrish, and Andreas Heßelmann. G.B. and Q.P.H. acknowledge support from
the Austrian Science Fund (FWF) under Projects No. M2641-N27 and No. M2751. M.L.
acknowledges support by the FWF under Project No. P29902-N27, and by the European
Research Council (ERC) Starting Grant No. 801770 (ANGULON). T.V.T. was supported
by the NSF CAREER award No. PHY-2045681. This work is supported by the German Research
Foundation (DFG) under Germany's Excellence Strategy EXC2181/1-390900948 (the Heidelberg
STRUCTURES Excellence Cluster). The authors acknowledge support by the state of
Baden-Württemberg through bwHPC.
article_number: '045115'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Giacomo
full_name: Bighin, Giacomo
id: 4CA96FD4-F248-11E8-B48F-1D18A9856A87
last_name: Bighin
orcid: 0000-0001-8823-9777
- first_name: Quoc P
full_name: Ho, Quoc P
id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87
last_name: Ho
orcid: 0000-0001-6889-1418
- first_name: Mikhail
full_name: Lemeshko, Mikhail
id: 37CB05FA-F248-11E8-B48F-1D18A9856A87
last_name: Lemeshko
orcid: 0000-0002-6990-7802
- first_name: T. V.
full_name: Tscherbul, T. V.
last_name: Tscherbul
citation:
ama: 'Bighin G, Ho QP, Lemeshko M, Tscherbul TV. Diagrammatic Monte Carlo for electronic
correlation in molecules: High-order many-body perturbation theory with low scaling.
Physical Review B. 2023;108(4). doi:10.1103/PhysRevB.108.045115'
apa: 'Bighin, G., Ho, Q. P., Lemeshko, M., & Tscherbul, T. V. (2023). Diagrammatic
Monte Carlo for electronic correlation in molecules: High-order many-body perturbation
theory with low scaling. Physical Review B. American Physical Society.
https://doi.org/10.1103/PhysRevB.108.045115'
chicago: 'Bighin, Giacomo, Quoc P Ho, Mikhail Lemeshko, and T. V. Tscherbul. “Diagrammatic
Monte Carlo for Electronic Correlation in Molecules: High-Order Many-Body Perturbation
Theory with Low Scaling.” Physical Review B. American Physical Society,
2023. https://doi.org/10.1103/PhysRevB.108.045115.'
ieee: 'G. Bighin, Q. P. Ho, M. Lemeshko, and T. V. Tscherbul, “Diagrammatic Monte
Carlo for electronic correlation in molecules: High-order many-body perturbation
theory with low scaling,” Physical Review B, vol. 108, no. 4. American
Physical Society, 2023.'
ista: 'Bighin G, Ho QP, Lemeshko M, Tscherbul TV. 2023. Diagrammatic Monte Carlo
for electronic correlation in molecules: High-order many-body perturbation theory
with low scaling. Physical Review B. 108(4), 045115.'
mla: 'Bighin, Giacomo, et al. “Diagrammatic Monte Carlo for Electronic Correlation
in Molecules: High-Order Many-Body Perturbation Theory with Low Scaling.” Physical
Review B, vol. 108, no. 4, 045115, American Physical Society, 2023, doi:10.1103/PhysRevB.108.045115.'
short: G. Bighin, Q.P. Ho, M. Lemeshko, T.V. Tscherbul, Physical Review B 108 (2023).
corr_author: '1'
date_created: 2023-08-06T22:01:10Z
date_published: 2023-07-15T00:00:00Z
date_updated: 2025-09-09T12:45:32Z
day: '15'
department:
- _id: MiLe
- _id: TaHa
doi: 10.1103/PhysRevB.108.045115
ec_funded: 1
external_id:
arxiv:
- '2203.12666'
isi:
- '001532067800001'
intvolume: ' 108'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2203.12666
month: '07'
oa: 1
oa_version: Preprint
project:
- _id: 26986C82-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02641
name: A path-integral approach to composite impurities
- _id: 26B96266-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02751
name: Algebro-Geometric Applications of Factorization Homology
- _id: 26031614-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: P29902
name: Quantum rotations in the presence of a many-body environment
- _id: 2688CF98-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '801770'
name: 'Angulon: physics and applications of a new quasiparticle'
publication: Physical Review B
publication_identifier:
eissn:
- 2469-9969
issn:
- 2469-9950
publication_status: published
publisher: American Physical Society
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Diagrammatic Monte Carlo for electronic correlation in molecules: High-order
many-body perturbation theory with low scaling'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 108
year: '2023'
...
---
_id: '10033'
abstract:
- lang: eng
text: The ⊗*-monoidal structure on the category of sheaves on the Ran space is not
pro-nilpotent in the sense of [3]. However, under some connectivity assumptions,
we prove that Koszul duality induces an equivalence of categories and that this
equivalence behaves nicely with respect to Verdier duality on the Ran space and
integrating along the Ran space, i.e. taking factorization homology. Based on
ideas sketched in [4], we show that these results also offer a simpler alternative
to one of the two main steps in the proof of the Atiyah-Bott formula given in
[7] and [5].
acknowledgement: 'The author would like to express his gratitude to D. Gaitsgory,
without whose tireless guidance and encouragement in pursuing this problem, this
work would not have been possible. The author is grateful to his advisor B.C. Ngô
for many years of patient guidance and support. This paper is revised while the
author is a postdoc in Hausel group at IST Austria. We thank him and the group for
providing a wonderful research environment. The author also gratefully acknowledges
the support of the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization
Homology,” Austrian Science Fund (FWF): M 2751.'
article_number: '107992'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Quoc P
full_name: Ho, Quoc P
id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87
last_name: Ho
orcid: 0000-0001-6889-1418
citation:
ama: Ho QP. The Atiyah-Bott formula and connectivity in chiral Koszul duality. Advances
in Mathematics. 2021;392. doi:10.1016/j.aim.2021.107992
apa: Ho, Q. P. (2021). The Atiyah-Bott formula and connectivity in chiral Koszul
duality. Advances in Mathematics. Elsevier. https://doi.org/10.1016/j.aim.2021.107992
chicago: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul
Duality.” Advances in Mathematics. Elsevier, 2021. https://doi.org/10.1016/j.aim.2021.107992.
ieee: Q. P. Ho, “The Atiyah-Bott formula and connectivity in chiral Koszul duality,”
Advances in Mathematics, vol. 392. Elsevier, 2021.
ista: Ho QP. 2021. The Atiyah-Bott formula and connectivity in chiral Koszul duality.
Advances in Mathematics. 392, 107992.
mla: Ho, Quoc P. “The Atiyah-Bott Formula and Connectivity in Chiral Koszul Duality.”
Advances in Mathematics, vol. 392, 107992, Elsevier, 2021, doi:10.1016/j.aim.2021.107992.
short: Q.P. Ho, Advances in Mathematics 392 (2021).
corr_author: '1'
date_created: 2021-09-21T15:58:59Z
date_published: 2021-09-21T00:00:00Z
date_updated: 2025-04-14T09:09:35Z
day: '21'
ddc:
- '514'
department:
- _id: TaHa
doi: 10.1016/j.aim.2021.107992
external_id:
arxiv:
- '1610.00212'
isi:
- '000707040300031'
file:
- access_level: open_access
checksum: f3c0086d41af11db31c00014efb38072
content_type: application/pdf
creator: qho
date_created: 2021-09-21T15:58:52Z
date_updated: 2021-09-21T15:58:52Z
file_id: '10034'
file_name: 1-s2.0-S000187082100431X-main.pdf
file_size: 840635
relation: main_file
file_date_updated: 2021-09-21T15:58:52Z
has_accepted_license: '1'
intvolume: ' 392'
isi: 1
keyword:
- Chiral algebras
- Chiral homology
- Factorization algebras
- Koszul duality
- Ran space
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
month: '09'
oa: 1
oa_version: Published Version
project:
- _id: 26B96266-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02751
name: Algebro-Geometric Applications of Factorization Homology
publication: Advances in Mathematics
publication_identifier:
eissn:
- 1090-2082
issn:
- 0001-8708
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: The Atiyah-Bott formula and connectivity in chiral Koszul duality
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 392
year: '2021'
...
---
_id: '9359'
abstract:
- lang: eng
text: "We prove that the factorization homologies of a scheme with coefficients
in truncated polynomial algebras compute the cohomologies of its generalized configuration
spaces. Using Koszul duality between commutative algebras and Lie algebras, we
obtain new expressions for the cohomologies of the latter. As a consequence, we
obtain a uniform and conceptual approach for treating homological stability, homological
densities, and arithmetic densities of generalized configuration spaces. Our results
categorify, generalize, and in fact provide a conceptual understanding of the
coincidences appearing in the work of Farb--Wolfson--Wood. Our computation of
the stable homological densities also yields rational homotopy types, answering
a question posed by Vakil--Wood. Our approach hinges on the study of homological
stability of cohomological Chevalley complexes, which is of independent interest.\r\n"
acknowledgement: "This paper owes an obvious intellectual debt to the illuminating
treatments of factorization homology by J.\r\nFrancis, D. Gaitsgory, and J. Lurie
in [GL,G1, FG]. The author would like to thank B. Farb and J. Wolfson for\r\nbringing
the question of explaining coincidences in homological densities to his attention.
Moreover, the author\r\nthanks J. Wolfson for many helpful conversations on the
subject, O. Randal-Williams for many comments which\r\ngreatly help improve the
exposition, and G. C. Drummond-Cole for many useful conversations on L∞-algebras.\r\nFinally,
the author is grateful to the anonymous referee for carefully reading the manuscript
and for providing\r\nnumerous comments which greatly helped improve the clarity
and precision of the exposition.\r\nThis work is supported by the Advanced Grant
“Arithmetic and Physics of Higgs moduli spaces” No. 320593 of\r\nthe European Research
Council and the Lise Meitner fellowship “Algebro-Geometric Applications of Factorization\r\nHomology,”
Austrian Science Fund (FWF): M 2751."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Quoc P
full_name: Ho, Quoc P
id: 3DD82E3C-F248-11E8-B48F-1D18A9856A87
last_name: Ho
orcid: 0000-0001-6889-1418
citation:
ama: Ho QP. Homological stability and densities of generalized configuration spaces.
Geometry & Topology. 2021;25(2):813-912. doi:10.2140/gt.2021.25.813
apa: Ho, Q. P. (2021). Homological stability and densities of generalized configuration
spaces. Geometry & Topology. Mathematical Sciences Publishers. https://doi.org/10.2140/gt.2021.25.813
chicago: Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration
Spaces.” Geometry & Topology. Mathematical Sciences Publishers, 2021.
https://doi.org/10.2140/gt.2021.25.813.
ieee: Q. P. Ho, “Homological stability and densities of generalized configuration
spaces,” Geometry & Topology, vol. 25, no. 2. Mathematical Sciences
Publishers, pp. 813–912, 2021.
ista: Ho QP. 2021. Homological stability and densities of generalized configuration
spaces. Geometry & Topology. 25(2), 813–912.
mla: Ho, Quoc P. “Homological Stability and Densities of Generalized Configuration
Spaces.” Geometry & Topology, vol. 25, no. 2, Mathematical Sciences
Publishers, 2021, pp. 813–912, doi:10.2140/gt.2021.25.813.
short: Q.P. Ho, Geometry & Topology 25 (2021) 813–912.
corr_author: '1'
date_created: 2021-05-02T06:59:33Z
date_published: 2021-04-27T00:00:00Z
date_updated: 2025-04-14T09:09:36Z
day: '27'
ddc:
- '514'
- '516'
- '512'
department:
- _id: TaHa
doi: 10.2140/gt.2021.25.813
ec_funded: 1
external_id:
arxiv:
- '1802.07948'
isi:
- '000682738600005'
file:
- access_level: open_access
checksum: 643a8d2d6f06f0888dcd7503f55d0920
content_type: application/pdf
creator: qho
date_created: 2021-05-03T06:54:06Z
date_updated: 2021-05-03T06:54:06Z
file_id: '9366'
file_name: densities.pdf
file_size: 479268
relation: main_file
success: 1
file_date_updated: 2021-05-03T06:54:06Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
issue: '2'
keyword:
- Generalized configuration spaces
- homological stability
- homological densities
- chiral algebras
- chiral homology
- factorization algebras
- Koszul duality
- Ran space
language:
- iso: eng
month: '04'
oa: 1
oa_version: Submitted Version
page: 813-912
project:
- _id: 25E549F4-B435-11E9-9278-68D0E5697425
call_identifier: FP7
grant_number: '320593'
name: Arithmetic and physics of Higgs moduli spaces
- _id: 26B96266-B435-11E9-9278-68D0E5697425
call_identifier: FWF
grant_number: M02751
name: Algebro-Geometric Applications of Factorization Homology
publication: Geometry & Topology
publication_identifier:
issn:
- 1364-0380
publication_status: published
publisher: Mathematical Sciences Publishers
quality_controlled: '1'
scopus_import: '1'
status: public
title: Homological stability and densities of generalized configuration spaces
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
year: '2021'
...