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Published August 15, 2013 | Published + Accepted Version
Journal Article Open

Thouless theorem for matrix product states and subsequent post density matrix renormalization group methods


The similarities between Hartree-Fock (HF) theory and the density matrix renormalization group (DMRG) are explored. Both methods can be formulated as the variational optimization of a wave-function Ansatz. Linearization of the time-dependent variational principle near a variational minimum allows to derive the random phase approximation (RPA). We show that the nonredundant parameterization of the matrix product state (MPS) tangent space [J. Haegeman, J. I. Cirac, T. J. Osborne, I. Pižorn, H. Verschelde, and F. Verstraete, Phys. Rev. Lett. 107, 070601 (2011)] leads to the Thouless theorem for MPS, i.e., an explicit nonredundant parameterization of the entire MPS manifold, starting from a specific MPS reference. Excitation operators are identified, which extends the analogy between HF and DMRG to the Tamm-Dancoff approximation (TDA), the configuration interaction (CI) expansion, and coupled cluster theory. For a small one-dimensional Hubbard chain, we use a CI-MPS Ansatz with single and double excitations to improve on the ground state and to calculate low-lying excitation energies. For a symmetry-broken ground state of this model, we show that RPA-MPS allows to retrieve the Goldstone mode. We also discuss calculations of the RPA-MPS correlation energy. With the long-range quantum chemical Pariser-Parr-Pople Hamiltonian, low-lying TDA-MPS and RPA-MPS excitation energies for polyenes are obtained.

Additional Information

© 2013 American Physical Society. Received 10 June 2013; published 12 August 2013. This research was supported by the Research Foundation Flanders (S.W.) and the National Science Foundation Grant No. SI2-SSE:1265277 (G.C.). The authors would like to thank Jutho Haegeman, Frank Verstraete, and Stijn De Baerdemacker for the many stimulating conversations.

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Accepted Version - 1305.1761.pdf

Published - PhysRevB.88.075122.pdf


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August 19, 2023
August 19, 2023