Grassmann Matrix Product States as a Tool for Ultracold-atom Model Systems

这个项目涉及理论超冷原子物理和量子信息理论之间的计算物理的基础研究。这是两个非常活跃的研究领域，被广泛认为是未来基于量子的技术的推动者，包括量子计算。该项目的主要目的是进一步发展描述非相对论连续模型系统的变分算法。这些算法可以用来描述具有质量不平衡的冷原子气体相互作用的模型系统，包括在光学晶格存在的情况下，和/或与费米子和玻色子的混合物。这项研究将与学生密切合作，以开放的方式进行。计划通过在研究生课程中纳入研究开发的计算工具以及在多个地点传播成果，包括向普通公众传播成果，来进行广泛传播。后者将与辛辛那提自然历史和科学博物馆合作，让学生参与他们在科学交流中的形成经验。新的连续矩阵-乘积状态(CMPS)ansatz将是拟议研究中的主要关注焦点。它构成了来自可积系统理论和量子信息论的张量网络方法的思想的汇合。此外，CMPS提供了一种从变分的角度看待一维量子场论(QFT)的新方法。它们提供了对强耦合QFT结构的有价值的非微扰见解，其基本性质渗透到物理学的许多不同分支。在使用冷原子的量子模拟的背景下发展这些新的理论和计算想法将带来额外的价值维度，并增加冷原子实验和多体理论之间日益增长的协同效应。在计算基础设施方面，该项目将利用俄亥俄州超级计算中心的资源。

This project involves basic research in computational physics at the interface between theoretical ultracold-atom physics and quantum-information theory. These are two very active areas of study, widely regarded as enablers for future quantum-based technologies, including quantum computation. The principal aim of the project is to further the development of variational algorithms for describing non-relativistic continuous model systems. These algorithms can be used to describe model systems of interacting cold-atom gases with mass-imbalance, including in the presence of optical lattices, and/or with mixtures of fermions and bosons. The research will be conducted in close collaboration with students and in an open manner. Broad dissemination is planned by including research-developed computational tools in graduate courses and by disseminating results in multiple venues, including to the general public. The latter will be done in collaboration with Cincinnati's Museum of Natural History and Science and involving students as part of their formative experience in science communication.The new continuum Matrix-Product States (cMPS) ansatz will be the main focus of attention in the proposed research. It constitutes the meeting of ideas coming from the theory of integrable systems and the tensor-network methods of quantum-information theory. Furthermore, cMPS brings in a new alternative to look at one-dimensional quantum field theories (QFTs) from a variational perspective. They provide valuable non-perturbative insights into the structure of strongly-coupled QFTs, whose fundamental nature permeates many different branches of physics. Developing these new theoretical and computational ideas in the context of quantum simulations using cold atoms will bring in an extra dimension of merit and add to the growing synergies between cold-atom experiments and many-body theories. In terms of computational infrastructure, the project will leverage the resources of the Ohio Supercomputing Center.