Chebyshev matrix product state approach for time evolution

Jad C. Halimeh, Fabian Kolley, and Ian P. McCulloch
Phys. Rev. B 92, 115130 – Published 14 September 2015

Abstract

We present and test a new algorithm for time-evolving quantum many-body systems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)]. The approach is based on merging the matrix product state (MPS) formalism with the method of expanding the time-evolution operator in Chebyshev polynomials. We calculate time-dependent observables of a system of hardcore bosons quenched under the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare the new algorithm to more standard methods using the MPS architecture. We find that the Chebyshev method gives numerically exact results for small times. However, the reachable times are smaller than the ones obtained with the other state-of-the-art methods. We further extend the new method using a spectral-decomposition-based projective scheme that utilizes an effective bandwidth significantly smaller than the full bandwidth, leading to longer evolution times than the nonprojective method and more efficient information storage, data compression, and less computational effort.

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  • Received 7 July 2015

DOI:https://doi.org/10.1103/PhysRevB.92.115130

©2015 American Physical Society

Authors & Affiliations

Jad C. Halimeh1, Fabian Kolley1, and Ian P. McCulloch2

  • 1Physics Department and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universität München, 80333 München, Germany
  • 2ARC Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland 4072, Australia

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Vol. 92, Iss. 11 — 15 September 2015

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