We present and test a new algorithm for time-evolving quantum many-bodysystems initially proposed by Holzner et al. [Phys. Rev. B 83, 195115 (2011)].The approach is based on merging the matrix product state (MPS) formalism withthe method of expanding the time-evolution operator in Chebyshev polynomials.We calculate time-dependent observables of a system of hardcore bosons quenchedunder the Bose-Hubbard Hamiltonian on a one-dimensional lattice. We compare thenew algorithm to more standard methods using the MPS architecture. We find thatthe Chebyshev method gives numerically exact results for small times. However,the reachable times are smaller than the ones obtained with the otherstate-of-the-art methods. We further extend the new method using aspectral-decomposition-based projective scheme that utilizes an effectivebandwidth significantly smaller than the full bandwidth, leading to longerevolution times than the non-projective method and more efficient informationstorage, data compression, and less computational effort.
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机译：我们提出并测试了Holzner等人最初提出的用于时间演化的量子多体系统的新算法。 [物理Rev. B 83，195115（2011）]。该方法基于将矩阵乘积状态（MPS）形式主义与扩展Chebyshev多项式中时间演化算子的方法相结合。我们计算硬核玻色子系统的时间相关可观性在Bose-Hubbard哈密顿量下在一维晶格上淬火。我们将新算法与使用MPS体系结构的更多标准方法进行比较。我们发现，切比雪夫方法在短时间内给出了数值精确的结果。但是，可达到的时间比使用其他最新方法获得的时间要短。我们使用基于方面分解的投影方案进一步扩展了该新方法，该方案使用的有效带宽明显小于全带宽，从而导致比非投影方法具有更长的演进时间，并且信息存储，数据压缩的效率更高，并且计算量更少。
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