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2024

Improving Perturbation Theory with the Sum-of-Squares: Third Order

Hastings, M. B.

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Understand

The sum-of-squares method can give rigorous lower bounds on the energy of quantum Hamiltonians.

Unfortunately, typically using this method requires solving a semidefinite program, which can be computationally expensive.
Further, the typically used degree-$4$ sum-of-squares (also known as the 2RDM method) does not correctly reproduce second order perturbation theory.
Here, we give a general method, an analogue of Wigner's $2n+1$ rule for perturbation theory, to compute the order of the error in a given sum-of-squares ansatz.

Improving Perturbation Theory with the Sum-of-Squares: Third Order · Around

Built on

A. J. Coleman, Reviews of Modern Physics 35
1963
Earlier work this paper cites.
R. M. Erdahl, International Journal of Quantum Chemistry 13
1978
Earlier work this paper cites.
J. Percus, International Journal of Quantum Chemistry 13
1978
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D. Mazziotti and R. Erdahl, Physical Review A 63
2001
Earlier work this paper cites.

Similar

M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, The Journal of Chemical Physics 114
2001
Cited alongside, same era.
A. Klyachko, 36
2006
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M. Nakata and K. Yasuda, Physical Review A—Atomic, Molecular, and Optical Physics 80
2009
Cited alongside, same era.
D. Mazziotti, Physical Review Letters 108
2012
Cited alongside, same era.

Then

R. O’Donnell, in 8th Innovations in Theoretical Computer Science Conference (ITCS 2017) (Schloss-Dagstuhl-Leibniz Zentrum für Informatik, 2017)
2017
Later among the works it cites.
M. B. Hastings, arXiv preprint arXiv:2205.12325 (2022)
Original
2022
Later among the works it cites.
M. B. Hastings and R. O’Donnell, in Proceedings of the 54th Annual ACM SIGACT Symposium on Theory of Computing (2022), pp. 776–789
2022
Later among the works it cites.

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