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Variational-Correlations Approach to Quantum Many-body Problems

Haim, Arbel and Kueng, Richard and Refael, Gil (2020) Variational-Correlations Approach to Quantum Many-body Problems. . (Unpublished)

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We investigate an approach for studying the ground state of a quantum many-body Hamiltonian that is based on treating the correlation functions as variational parameters. In this approach, the challenge set by the exponentially-large Hilbert space is circumvented by approximating the positivity of the density matrix, order-by-order, in a way that keeps track of a limited set of correlation functions. In particular, the density-matrix description is replaced by a correlation matrix whose dimension is kept linear in system size, to all orders of the approximation. Unlike the conventional variational principle which provides an upper bound on the ground-state energy, in this approach one obtains a lower bound instead. By treating several one-dimensional spin 1/2 Hamiltonians, we demonstrate the ability of this approach to produce long-range correlations, and a ground-state energy that converges to the exact result. Possible extensions, including to higher-excited states are discussed.

Item Type:Report or Paper (Discussion Paper)
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Additional Information:We have benefited from discussions with Y. Baum, O. Motrunich, E. P. L. van Nieuwenburg, K. Slagel, and C. D. White. This research was supported by the Institute of Quantum Information and Matter, an NSF Frontier center funded by the Gordon and Betty Moore Foundation, the Packard Foundation, and the Simons foundation. AH acknowledges support from the Walter Burke Institute for Theoretical Physics at Caltech. RK acknowledges funding provided by the Office of Naval Research (Award N00014-17-1-2146) and the Army Research Office (Award W911NF121054).
Group:UNSPECIFIED, Institute for Quantum Information and Matter, Walter Burke Institute for Theoretical Physics
Funding AgencyGrant Number
Institute of Quantum Information and Matter (IQIM)UNSPECIFIED
Gordon and Betty Moore FoundationUNSPECIFIED
David and Lucile Packard FoundationUNSPECIFIED
Simons FoundationUNSPECIFIED
Walter Burke Institute for Theoretical Physics, CaltechUNSPECIFIED
Office of Naval Research (ONR)N00014-17-1-2146
Army Research Office (ARO)W911NF121054
Record Number:CaltechAUTHORS:20200303-081122185
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:101670
Deposited By: Tony Diaz
Deposited On:03 Mar 2020 19:07
Last Modified:04 Jun 2020 10:14

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