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Standard variational methods tend to obtain upper bounds on the ground state energy of quantum many-body systems.
P. W. Anderson, Phys. Rev. 83
1951
Earlier work this paper cites.
K. Husimi, Proc. Phys. Math. Soc. Japan 22
1955
Earlier work this paper cites.
A.J. Coleman, Rev. Mod. Phys. 35
1963
Earlier work this paper cites.
C. Garrod and J. Percus, J. Math. Phys. 5
1964
Earlier work this paper cites.
P.H. Calamai and J.J. Mor e ´ \acute{e} , Math. Prog. 39
1987
Earlier work this paper cites.
R.A. Horn and C.R. Johnson, Matrix analysis
1991
Earlier work this paper cites.
S.R. White, Phys. Rev. Lett. 69
1992
Earlier work this paper cites.
L. Vandenberghe and S. Boyd, SIAM Rev. 38
1996
Earlier work this paper cites.
S. Östlund and S. Rommer, Phys. Rev. Lett. 75
1997
Earlier work this paper cites.
M. Takahashi, Thermodynamics of one-dimensional solvable models
1999
Earlier work this paper cites.
D.A. Mazziotti and R.M. Erdahl, Phys. Rev. A 63
2001
Cited alongside, same era.
F. Deutsch, Best approximation in inner product spaces
2001
Cited alongside, same era.
D.A. Mazziotti, Phys. Rev. Lett. 93
2004
Cited alongside, same era.
G. Gidofalvi and D.A. Mazziotti, Phys. Rev. A 69
2004
Cited alongside, same era.
J. Dattorro, Convex Optimization & Euclidean Distance Geometry
2005
Cited alongside, same era.
E.G. Birgin and M. Raydan, SIAM J. Sci. Comput. 26
2005
Cited alongside, same era.
G. Gidofalvi and D.A. Mazziotti, Phys. Rev. A 72
2005
Cited alongside, same era.
S. Pironio, M. Navascues and A. Acin, SIAM J. Optim. 20
2008
Later among the works it cites.
M. Reuter, Entanglement Properties of Strongly Correlated Spin Systems
2008
Later among the works it cites.
S. Boyd and L. Vandenberghe, Convex Optimization
2009
Later among the works it cites.
C.A. Schwerdtfeger and D.A. Mazziotti, J. Chem. Phys. 130
2009
Later among the works it cites.
T. Baumgratz, Diploma Thesis, University Ulm, Germany 2010
2010
Later among the works it cites.
A.V. Sinitskiy, L. Greenman, D.A. Mazziotti, J. Chem. Phys. 133
2010
Later among the works it cites.
U. Schollwoeck, Ann. Phys. 326
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J.R. Hammond and D.A. Mazziotti, Phys. Rev. A 73
2006
Cited alongside, same era.
D.A. Mazziotti, Ed., Reduced-density-matrix mechanics: with application to many-electron atoms and molecules
2007
Cited alongside, same era.
Indeed, it seems that lim α → ∞ P 𝒞 ( X − α G ) = X ∗ \lim_{\alpha\rightarrow\infty}P_{\mathcal{C}}\left(X-\alpha G\right)=X^{*} holds, where X ∈ ℋ X\in\mathcal{H} is the initial matrix and X ∗ ∈ 𝒞 X^{*}\in\mathcal{C} is such that it minimizes the function E ( X ) E\left(X\right) on the convex set 𝒞 \mathcal{C} , i.e. E ( X ∗ ) ≤ E ( X ) E\left(X^{*}\right)\leq E\left(X\right) for all X ∈ 𝒞 X\in\mathcal{C}
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2011
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D.A. Mazziotti, Phys. Rev. Lett. 106
2011
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J. Cai, Private Communication (2011)
2011
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