Matrix-Product-State Open Source Code and the Many Body Physics of Ultracold Molecules

我们将开发一维纠缠量子多体系统的矩阵积态（MPS）编码，包括远程相互作用，这是超冷分子固有的远程偶极-偶极相互作用所必需的。作为ALPS合作的一部分，我们的开源代码将集成到ALPS（物理模拟算法和库）包中。随着更复杂的分子接近量子简并，描述它们的多体模型的数量和复杂性也将大幅增加。此外，搜索诸如量子顺序之类的紧急现象需要探索巨大的参数空间，并使用许多不同的系统大小进行外推。这要求我们重新思考我们设计和调度模拟以及收集和解释数据的方式。要产生长期影响的开源工具必须具有灵活性，以适应不同的物理自由度、不同的哈密顿量和不同的动态过程；它们必须能够有效地管理大参数探索；它们必须包含从大型模拟中提取数据的强大工具。我们提出的MPS算法使我们能够应对这些挑战，并为下一波超冷分子物理做好准备。我们为矩阵积态（MPS）和相关方法创建的开源代码有可能为强相关系统提供新的见解，强相关系统是物理学中的一个长期问题，到目前为止我们只能取得一点进展。强相关系统包括高温超导体，这是能源技术的一个突出问题，因为相当大一部分能源资源仅仅浪费在输电线路上；高温材料有可能减轻这种损失。MPS方法使我们能够探索量子计算机的不同模型，包括应用于量子计算的超冷分子的主要物理学科。最后，在严格的数值技术和高性能并行计算方面对学生进行培训是在社会许多领域取得成功的关键，从空间方案到全球气候变化，再到监测和管理全国范围内的传染病爆发。该奖项将支持这种培训，并将支持从本科到研究生阶段参与这项工作的首席研究员。

We will develop matrix product state (MPS) codes for entangled quantum many-body systems in one spatial dimension including long-range interactions, necessary for the long-range dipole-dipole interaction inherent to ultracold molecules. Our open source codes will be integrated into the ALPS (Algorithms and Libraries for Physics Simulations) package as part of the ALPS collaboration. As more complex molecules approach quantum degeneracy, the number and complexity of many-body models to describe them will also increase substantially. Additionally, searching for emergent phenomena such as quantum order requires exploration of vast parameter spaces and extrapolation using many different system sizes. This requires us to rethink the way in which we design and dispatch simulations and collect and interpret data. Open source tools which are to have a long term impact must be flexible to adapt to different physical degrees of freedom, different Hamiltonians, and different dynamical processes; they must be efficient to manage large parameter exploration; and they must contain powerful tools for extracting data from large simulations. Our proposed MPS algorithms enable us to meet these challenges and be prepared for the next wave of ultracold molecular physics.Our creation of open source code for matrix product state (MPS) and related methods has the potential for new insights into strongly correlated systems, a standing problem in physics on which we have been able to make only a little progress so far. Strongly correlated systems include high-temperature superconductors, an outstanding problem for energy technology as a sizeable fraction of energy resources are squandered simply in transmission lines; high-temperature materials have the potential to alleviate this loss. MPS methods allow us to explore different models of a quantum computer, including in our main physical subject of ultracold molecules, applied to quantum computing. Finally, the training of students in rigorous numerical techniques and high-performance parallel computing is key to success in a number of arenas in society, from the space program to global climate change to monitoring and managing nation-wide outbreaks of infectious diseases. This award will support such training, and will support a principal investigator involved in that effort from the undergraduate through graduate levels.