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 non-projective method and more efficient information
storage, data compression, and less computational effort.Comment: 14 pages, 8 figure
