- S. Di Palmaet al.,J. Proteome Res. 10 , 3814–3819 (2011).
- J. C. Tranet al.,Nature 480 , 254–258 (2011).
- A. I. Nesvizhskii, R. Aebersold,Mol. Cell. Proteomics 4 ,
1419 – 1440 (2005). - L. M. Smith, N. L. Kelleher,Science 359 , 1106–1107 (2018).
- K. A. Brown, J. A. Melby, D. S. Roberts, Y. Ge,Expert Rev.
Proteomics 17 , 719–733 (2020). - R. D. LeDucet al.,Mol. Cell. Proteomics 18 , 796– 805
(2019). - V. N. Uversky,Int. J. Mol. Sci. 17 , 1874 (2016).
- R. Aebersoldet al.,Nat. Chem. Biol. 14 , 206– 214
(2018). - L. M. Smithet al.,Sci. Adv. 7 , eabk0734 (2021).
- I. Ntaiet al.,Mol. Cell. Proteomics 15 , 45–56 (2016).
- M. Stovskyet al.,J. Urol. 201 , 1115–1120 (2019).
- J. Levitskyet al.,Clin. Gastroenterol. Hepatol. 15 , 584–593.e2
(2017). - A. Moreau, E. Varey, I. Anegon, M. C. Cuturi,Cold Spring Harb.
Perspect. Med. 3 , a015461 (2013). - V. Ronca, G. Wootton, C. Milani, O. Cain,Front. Immunol. 11 ,
2155 (2020). - J. A. Ponset al.,Transplantation 86 , 1370–1378 (2008).
- M. Romano, G. Fanelli, C. J. Albany, G. Giganti, G. Lombardi,
Front. Immunol. 10 , 43 (2019). - T. K. Tobyet al.,Am. J. Transplant. 17 , 2458– 2467
(2017). - J. Levitskyet al.,Am. J. Transplant. 20 , 2173–2183 (2020).
- J. Levitskyet al.,Transplantation10.1097/TP.0000000000003895
(2021). - J. Levitskyet al.,Am. J. Transplant.ajt.16835 (2021).
- Y. Zhouet al.,Nat. Commun. 10 , 1523 (2019).
- R. El Masri, J. Delon,Nat. Rev. Immunol. 21 , 499– 513
(2021). - W. Witkeet al.,EMBO J. 17 , 967–976 (1998).
- A. Ramjiet al.,Liver Transpl. 8 , 945–951 (2002).
- T. Uemuraet al.,Clin. Transplant. 22 , 316–323 (2008).
- P. H. Thurairajahet al.,Transplantation 95 , 955–959 (2013).
- C. R. Kleiveland, inThe Impact of Food Bioactives on Health:
In Vitro and Ex Vivo Models, K. Verhoeckxet al., Eds. (Springer,
2015), pp. 161–167. - S. K. Gupta, T. Hassel, J. P. Singh,Proc. Natl. Acad. Sci. U.S.A.
92 , 7799–7803 (1995). - H. Guo, Y. Wang, Z. Zhao, X. Shao,Scand. J. Immunol. 81 ,
129 – 134 (2015). - H. K. Drescheret al.,Front. Physiol. 10 , 326 (2019).
- R. Schoppmeyeret al.,Eur. J. Immunol. 47 , 1562– 1572
(2017). - T. Stuartet al.,Cell 177 , 1888–1902.e21 (2019).
ACKNOWLEDGMENTS
The authors thank N. Haverland and the following members of the
Robert H. Lurie Comprehensive Cancer Center Flow Cytometry
Core Facility for helpful discussions and experimental assistance
with FACS methodology: S. Swaminathan, P. Mehl, and C. Ostiguin.
We thank P. Oksvold for discussions and assistance with making
the HPA Blood Cell Atlas data available. Analysis of these
transcriptomic data was performed on resources provided by the
Swedish National Infrastructure for Computing (SNIC) through
Uppsala Multidisciplinary Center for Advanced Computational
Science (UPPMAX) under project sens2019032. We also thank
L. M. Smith for additional computational resources for proteomic
analysis with MetaMorpheus.Funding:Funding was provided by
Paul G. Allen Frontiers Program award 11715 (N.L.K.); HuBMAP
grant UH3 CA246635-02 (N.L.K.); the National Institute of General
Medical Sciences of the National Institutes of Health under grants
P41 GM108569 (N.L.K.), R21LM013097 (P.M.T.), T32 GM105538
(T.K.T.), and R21 AI135827 (J.L.); Knut and Alice Wallenberg
Foundation grant 2016.0204 (A.J.C. and E.L.); and Swedish
Research Council grant 2017-05327 (E.L.). A portion of this work
was performed at the Ion Cyclotron Resonance User Facility at the
National High Magnetic Field Laboratory, which is supported by
the National Science Foundation Division of Materials Research and
Division of Chemistry through DMR-1644779, and the State of
Florida.Author contributions:Conceptualization: N.L.K., P.M.T.,
and J.L. Methodology: R.D.M., V.R.G., T.K.T., K.S., J.E.H., N.L.K.,
P.M.T., and J.L. Investigation: R.D.M., V.R.G., J.W.S., T.K.T., J.E.H.,
F.N., H.S.S., K.S., L.F., J.M.C., C.J.D., E.F., S.E.A., L.C.A., D.S.B.,
C.L.H., and A.J.C. Visualization: R.D.M., V.R.G., T.K.T., K.S., J.E.H.,
and F.N. Data curation: R.D.M., R.D.L., A.J.C., J.B.G., R.T.F., M.T.R.,
and P.M.T. Formal analysis: R.D.M, V.R.G., F.N., H.S.S., R.D.L.,
A.J.C., J.B.G., R.T.F., M.T.R., and P.M.T. Software: R.D.M., V.R.G.,
H.S.S., R.D.L., A.J.C., J.B.G., R.T.F., M.T.R., and P.M.T. Resources:
N.L.K., J.L., E.L., C.L.H., and A.I.K. Funding acquisition: N.L.K.,
P.M.T., E.L., and J.L. Writing–original draft: R.D.M., V.R.G., N.L.K.,
P.M.T., R.D.L., L.C.A., E.F., and J.L. Writing–review & editing:
R.D.M., V.R.G., N.L.K., P.M.T., R.D.L., L.C.A., and J.L.Competing
interests:N.L.K. is involved in entrepreneurial activities in top-
down proteomics and consults for Thermo Fisher Scientific. A.I.K.
is an employee of Stem Cell Technologies.Data and materials
availability:All cell types and cell enrichment kits used are
commercially available and listed in the material and methods
section of the supplementary materials. All .raw files are available
at the Proteomics Identifications Database (PRIDE; http://www.ebi.ac.uk/
pride/) under accession numbers PXD026123 to PXD026178.
Proteoform information is available in the Blood Proteoform Atlas
(https://blood-proteoform-atlas.org).SUPPLEMENTARY MATERIALS
science.org/doi/10.1126/science.aaz5284
Materials and Methods
Supplementary Text
Figs. S1 to S7
Tables S1 to S12
References ( 47 Ð 76 )
MDAR Reproducibility Checklist12 June 2021; accepted 17 December 2021
10.1126/science.aaz5284QUANTUM CRITICALITYQuantum critical points and the sign problem
R. Mondaini^1 , S. Tarat^1 , R. T. Scalettar^2The“sign problem”(SP) is a fundamental limitation to simulations of strongly correlated matter.
It is often argued that the SP is not intrinsic to the physics of particular Hamiltonians because its
behavior can be influenced by the choice of algorithm. By contrast, we show that the SP in
determinant quantum Monte Carlo (QMC) is quantitatively linked to quantum critical behavior.
We demonstrate this through simulations of several models with critical properties that are
relatively well understood. We propose a reinterpretation of the low average sign for the Hubbard
model on the square lattice away from half filling in terms of the onset of pseudogap behavior
and exotic superconductivity. Our study charts a path for exploiting the average sign in QMC
simulations to understand quantum critical behavior.O
ver the past several decades, quantum
Monte Carlo (QMC) simulations have
provided great insight into challenging
strong correlation problems in chem-
istry ( 1 , 2 ), condensed-matter physics
( 3 , 4 ), nuclear physics ( 5 ), and high-energy
physics ( 6 ). In all of these areas, however, the
sign problem (SP), which occurs when the
probability for specific quantum configura-
tions in the importance sampling becomes
negative, substantially constrains their ap-
plication. Solving, or at least mitigating, the
SP is one of the central endeavors of com-
putational physics. The extent and impor-
tance of the effort is indicated by the many
proposed solutions and their continued de-
velopment over the past three decades [for
an overview, see the supplementary mate-
rials ( 7 ) and references therein].
Despite enormous effort, the SP remains
unsolved. In fact, the lack of progress is one
of the main driving forces behind a number
of large-scale research efforts, including the
quest for quantum emulators ( 8 – 10 ) and quan-
tum computing itself ( 11 , 12 ). One of the most
fundamental mysteries concerns the possible
link between the SP and the underlying phys-
ics of the Hamiltonian being investigated.Here, instead of challenging this nondeter-
ministic polynomial hard problem ( 13 ) or
proposing solutions that can partially ame-
liorate its behavior ( 14 , 15 ), we show that there
is a clear connection between the behavior
of the average signhSiin the widely used
determinant quantum Monte Carlo (DQMC)
method and several quantum phase transitions
(QPTs): that of the semimetal to antiferromag-
netic Mott insulator (MI) of Dirac fermions
in the spinful [SU(2)] honeycomb-Hubbard
Hamiltonian ( 16 , 17 ), the band to correlated
insulator transition ( 18 – 20 ), and charge den-
sity wave (CDW) transitions of spinless [U(1)]
fermions on a honeycomb lattice ( 21 , 22 ). In
the first example, simulations at half-filling,
where the quantum critical point (QCP) oc-
curs, are SP-free. We introduce a small doping
mand show, in the limitm→ 0 +at temperature
T→0, thathSievolves rapidly as we tune
through the QCP.
Our second illustration, the ionic Hubbard
model, has an SP even at half-filling. Here,
the average sign undergoes an abrupt drop
at the band insulator (BI) to correlated metal
(CM) transition. The third example, spinless
fermions on a honeycomb lattice, also features
a semimetal to (charge) insulator transition
butallowsforanSP-freeapproach.Studyingit
with a method that contains an“unnecessary”
SP lends insight into the key question of the
influence of different algorithms on the con-
nection between the SP and the physics of
model Hamiltonians.418 28 JANUARY 2022•VOL 375 ISSUE 6579 science.orgSCIENCE
(^1) Beijing Computational Science Research Center, Beijing
100193, China.^2 Department of Physics, University of
California, Davis, CA 95616, USA.
Correspondence: [email protected] (R.M.); [email protected]
(S.T.); [email protected] (R.T.S.)
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