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

ORAL

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 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.

*This research was enabled in part by support provided by Calcul Qu\'ebec (www.calculquebec.ca) and Compute Canada (www.computecanada.ca). This project was undertaken on the Viking Cluster, which is a high performance compute facility provided by the University of York. We are grateful for computational support from the University of York High Performance Computing service, Viking and the Research Computing team.This work has been supported in part by the Natural Sciences and Engineering Research Council of Canada (NSERC) under grants RGPIN-2015-05598 and RGPIN-2020-05060.T.E.B.~thanks funding provided by the postdoctoral fellowship from Institut quantique and Institut Transdisciplinaire d'Information Quantique (INTRIQ). This research was undertaken thanks in part to funding from the Canada First Research Excellence Fund (CFREF). T.E.B.~is grateful to the US-UK Fulbright Commission for financial support under the Fulbright U.S. Schol

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Presenters

  • Thomas E Baker

    • University of York

Authors

  • David Sénéchal

    • Université de Sherbrooke

  • Alexandre Foley

    • Universite de Sherbrooke
    • Université de Sherbrooke

  • Thomas E Baker

    • University of York