Open source Matrix Product States: Opening ways to simulate entangled many-body quantum systems in one dimension

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.

数值模拟是研究无法严格解析求解、缺乏解析表达式的量子系统的有力工具。针对一维纠缠量子系统，张量网络方法（其中矩阵乘积态（Matrix Product States, MPS）是其重要分支）已受到量子物理多个研究领域的广泛关注，研究范畴涵盖固态系统、量子模拟器与量子计算等方向。本开源MPS代码为科研社区提供了一套用于分析一维量子系统静力学与动力学特性的工具集。本文介绍我们开发的开源矩阵乘积态库（Open Source Matrix Product States, OSMPS），该库基于Python与Fortran2003语言实现了一系列MPS相关方法。该库包含基于变分近似的基态与激发态计算工具，同时支持具备平移不变性的无限长系统基态求解。动力学模拟模块集成多种算法，其中三款算法可兼容长程相互作用体系。该库的便捷特性包括：内置对费米子系统的支持；针对有限系统，可实现基于旋转U(1)对称性与离散Z_2对称性的粒子数守恒约束；同时支持基于消息传递接口（Message Passing Interface, MPI）的数据并行计算。本文阐述了该库所采用的核心原理与技术细节，并辅以具体示例展示如何通过通用接口高效分析伊辛（Ising）模型与玻色-哈伯德（Bose–Hubbard）模型。本说明文档涵盖模拟任务的前置准备、调度执行与后处理等全流程环节。