Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension
Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension
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DOI：
10.1016/j.cpc.2017.12.015
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发表时间：
2018-04-01
影响因子：
6.3
通讯作者：
Carr, Lincoln D.
中科院分区：
文献类型：
--
作者：
Jaschke, Daniel;Wall, Michael L.;Carr, Lincoln D.
数值模拟是研究量子系统的有力工具，它超越了缺乏解析表达式的精确可解系统。对于一维纠缠量子系统，张量网络方法，其中包括矩阵积态（mps），已经引起了从固态系统到量子模拟器和量子计算等量子物理不同领域的兴趣。我们的开源MPS代码为社区提供了一个工具集来分析一维量子系统的静力学和动力学。在这里，我们展示了用Python和Fortran2003实现的MPS方法的开源库——开源矩阵产品状态（open source Matrix Product States， OSMPS）。该库包括通过变分分析计算基态和激发态的工具。我们也支持具有平移不变性的无限系统的基态。用不同的算法模拟了动力学，包括三种支持远程交互的算法。方便的功能包括内置支持费米子系统和有限系统的旋转U(1)和离散Z(2)对称的数字守恒，以及MPI的数据并行性。我们解释了这个库中使用的原理和技术，以及如何有效地使用通用接口来分析Ising和Bose-Hubbard模型的示例。这个描述包括模拟的准备以及它们的调度和后处理。程序摘要程序标题：开源矩阵产品状态（OSMPS）， v2.0程序文件doi: http://dx.doi.org/10.17632/vxm2mcmk4v.1Licensing规定：GNU GPL v3编程语言：Python， Fortran2003， MPI并行计算编译器（Fortran）： gfortran, ifort， g95依赖关系：除了Fortran编译器的最低要求是BIAS， LAPACK， ARPACK, Python, numpy, scipy。用于绘图的其他包包括matplotlib、dvipng和LATEX包。要使用本地龙格-库塔时间演化，需要在主页http://www.maths.uq.edu.au/expokit/上提供的Expokit包。补充材料：我们提供程序来复制附录中选定的数字。问题性质：求解多体纠缠量子系统的基态和动力学是一个具有挑战性的问题；希尔伯特空间随系统大小呈指数增长。希尔伯特空间对浮点精度的完全对角化被限制在小于40个量子位。求解方法：通过截断希尔伯特空间中最不重要的部分，在一维空间中的矩阵积态克服指数增长的希尔伯特空间。误差可以很好地控制。为了使整个系统的能量最小化，局部邻近的站点进行了变分优化。我们可以瞄准基态和低洼激发态。此外，我们还提供了求解多体薛定谔方程时间演化的各种方法。这些方法包括使用局部传播子的Suzuki-Trotter分解或Krylov方法，两者都在完全Hilbert空间上逼近传播子。(C) 2017 Elsevier B.V.版权所有
Numerical simulations are a powerful tool to study quantum systems beyond exactly solvable systems lacking an analytic expression. For one-dimensional entangled quantum systems, tensor network methods, amongst them Matrix Product States (MPSs), have attracted interest from different fields of quantum physics ranging from solid state systems to quantum simulators and quantum computing. Our open source MPS code provides the community with a toolset to analyze the statics and dynamics of one-dimensional quantum systems. Here, we present our open source library, Open Source Matrix Product States (OSMPS), of MPS methods implemented in Python and Fortran2003. The library includes tools for ground state calculation and excited states via the variational ansatz. We also support ground states for infinite systems with translational invariance. Dynamics are simulated with different algorithms, including three algorithms with support for long-range interactions. Convenient features include built-in support for fermionic systems and number conservation with rotational U(1) and discrete Z(2) symmetries for finite systems, as well as data parallelism with MPI. We explain the principles and techniques used in this library along with examples of how to efficiently use the general interfaces to analyze the Ising and Bose-Hubbard models. This description includes the preparation of simulations as well as dispatching and post-processing of them.Program summaryProgram title: Open Source Matrix Product States (OSMPS), v2.0Program Files doi: http://dx.doi.org/10.17632/vxm2mcmk4v.1Licensing provisions: GNU GPL v3Programming language: Python, Fortran2003, MPI for parallel computingCompilers (Fortran): gfortran, ifort, g95Dependencies: The minimal requirements in addition to the Fortran compiler are BIAS, LAPACK, ARPACK, python, numpy, scipy. Additional packages for plotting include matplotlib, dvipng, and LATEX packages. The Expokit package, available at the homepage http://www.maths.uq.edu.au/expokit/, is required to use the Local Runge-Kutta time evolution.Supplementary material: We provide programs to reproduce selected figures in the Appendices.Nature of problem: Solving the ground state and dynamics of a many-body entangled quantum system is a challenging problem; the Hilbert space grows exponentially with system size. Complete diagonalization of the Hilbert space to floating point precision is limited to less than forty qubits.Solution method: Matrix Product States in one spatial dimension overcome the exponentially growing Hilbert space by truncating the least important parts of it. The error can be well controlled. Local neighboring sites are variationally optimized in order to minimize the energy of the complete system. We can target the ground state and low lying excited states. Moreover, we offer various methods to solve the time evolution following the many-body Schrodinger equation. These methods include e.g. the Suzuki-Trotter decompositions using local propagators or the Krylov method, both approximating the propagator on the complete Hilbert space. (C) 2017 Elsevier B.V. All rights reserved.