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Chebyshev matrix product state approach for time evolution

机译：切比雪夫矩阵产品状态的时间演化方法

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摘要

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.
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。 [物理修订版B 83,195115（2011）。该方法基于将矩阵乘积状态（MPS）形式主义与在Chebyshev多项式中扩展时间演化算符的方法合并。我们计算一维晶格上玻色-哈伯德哈密顿量下淬火的铁杆玻色子系统的时变可观性。我们将新算法与使用MPS架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，可到达的时间比用其他最新方法获得的时间要短。我们使用基于频谱分解的投影方案进一步扩展了该新方法，该方案利用的有效带宽明显小于全带宽，与非投影方法相比，进化时间更长，信息存储，数据压缩效率更高，计算工作量更少。

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  • 来源
    《Physical review》 |2015年第11期|115130.1-115130.13|共13页
  • 作者

    Jad C. Halimeh; Fabian Kolley; Ian P. McCulloch;

  • 作者单位

    Physics Department and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universitaet Muenchen, 80333 Muenchen, Germany;

    Physics Department and Arnold Sommerfeld Center for Theoretical Physics, Ludwig-Maximilians-Universitaet Muenchen, 80333 Muenchen, Germany;

    ARC Centre for Engineered Quantum Systems, School of Mathematics and Physics, The University of Queensland, St. Lucia, Queensland 4072, Australia;

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  • 正文语种 eng
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  • 关键词

    spin chain models; numerical simulation studies; models based on group theory; boson systems;

    机译：自旋链模型;数值模拟研究;基于群体理论的模型;玻色子系统;

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