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Direct solution of multiple excitations in a matrix product state with block Lanczos

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Listed:
  • Thomas E. Baker

    (Université de Sherbrooke
    University of York
    University of Victoria)

  • Alexandre Foley

    (Université de Sherbrooke)

  • David Sénéchal

    (Université de Sherbrooke)

Abstract

Matrix product state methods are known to be efficient for computing ground states of local, gapped Hamiltonians, particularly in one dimension. We introduce the multi-targeted density matrix renormalization group method that acts on a bundled matrix product state, holding many excitations. The use of a block or banded Lanczos algorithm allows for the simultaneous, variational optimization of the bundle of excitations. The method is demonstrated on a Heisenberg model and other cases of interest. A large of number of excitations can be obtained at a small bond dimension with highly reliable local observables throughout the chain. Graphical abstract

Suggested Citation

  • Thomas E. Baker & Alexandre Foley & David Sénéchal, 2024. "Direct solution of multiple excitations in a matrix product state with block Lanczos," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 97(6), pages 1-18, June.
    • Handle: RePEc:spr:eurphb:v:97:y:2024:i:6:d:10.1140_epjb_s10051-024-00702-7
    DOI: 10.1140/epjb/s10051-024-00702-7
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    References listed on IDEAS

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    1. C. Degli Esposti Boschi & F. Ortolani, 2004. "Investigation of quantum phase transitions using multi-target DMRG methods," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 41(4), pages 503-516, October.
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