New Perspectives in Strongly Interacting Systems: preparing for quantum gauge simulators.

强相互作用系统中非微扰物理的第一性原理研究是一个具有挑战性的研究领域。它影响了广泛的领域，从超越粒子物理标准模型的新物理学，到量子色动力学（QCD），甚至到天体物理学对象，如中子星。在更好地理解系统的基础上开发新的算法有助于提高蒙特卡罗方法的适用性。即便如此，许多有趣的问题，特别是实时进化问题，都超出了现有数值技术的范围，需要新的方法来取得进展。为了对新方法进行基准测试，现有的工具仍然发挥着至关重要的作用。量子模拟是近二十年来迅速发展起来的一种新方法。量子模拟器是用于模拟特定物理系统的专用量子计算机，通过光学晶格中的冷原子或离子阱中的离子来实现。一旦它们起作用，它们在某些问题上的表现将远远超过传统的同类产品。在凝聚态物理中已经存在几个这样的例子，并且正在越来越多地开发用于粒子物理应用。与现有的理论和蒙特卡罗方法一起，它们有很大的潜力来增加我们对强相关系统的理解。本项目将考虑一些与量子cd相关的物理量子模拟器。某些具有有限维希尔伯特空间的晶格规范理论（称为量子链路模型）是在光学晶格中实现的理想候选者。研究将侧重于所考虑模型的量子模拟，以及经典模拟算法的开发，以对这些量子模拟器进行基准测试，特别是使用静态特性。动态特性的研究，比如实时进化，可以用量子模拟器来研究。这些模型在实验室中的实现只是近似的。开发的经典算法将解释这一点。此外，本项目将研究是否可以用量子链路模型实现连续体场论。这对连续统规范理论的量子模拟器的研究进展具有重要的影响。此外，同样的经典模拟算法可以解决d ~ 2维共形场理论的某些方面。这可以为新的数值和分析方法（如保形自举）提供独立的检查。洪堡大学和DESY Zeuthen优秀的当地科学环境，以及PI与奥地利因斯布鲁克大学原子物理学家的密切联系，预计将有助于拟议项目的成功，并对上述领域产生重大影响。

A first-principles study of the non-perturbative physics in strongly interacting systems is a challenging field of research. It impacts a wide variety of areas, from new physics beyond the Standard Model of particle physics, to Quantum Chromodynamics (QCD), and even to astrophysical objects, such as neutron stars. Development of new algorithms based on the better understanding of the system helps in improved applicability of Monte Carlo methods. Even so, many interesting problems, particularly that of real-time evolution, are beyond the scope of present numerical techniques, and need new methods to make progress. The existing tools still play a crucial role in order to benchmark the new methods. Quantum simulation is a new method, which has rapidly developed in the past two decades. Quantum simulators are special purpose quantum computers to emulate specific physical systems, realized with cold atoms in optical lattices or ions trapped in ion traps. Once they work, they will by far outperform their classical counterparts for certain problems. Several such examples already exist in condensed matter physics and are being increasingly developed for particle physics applications. Together with existing theoretical and Monte Carlo methods, they have a great potential for increasing our understanding of strongly correlated systems. This project will consider some quantum simulators relevant for QCD-related physics. Certain lattice gauge theories (called quantum link models) with finite dimensional Hilbert spaces are ideal candidates to be implmented in optical lattices. The research will focus on the quantum simulation of the considered models, together with the development of classical simulation algorithmsfor benchmarking these quantum simulators, particularly using the static properties. The study of dynamical properties, like real-time evolution, can then be studied with quantum simulators. Realization of these models in the laboratories are only approximate. The classical algorithms developed will account for this. Additionally, this project will study whether continuum field theories can be realized with the quantum link models. This has crucial impact on the progress of quantum simulators for continuum gauge theories. Moreover, the same classical simulation algorithms can address some aspects of conformal field theories in dimensions d > 2. This can provide an independent check of new numerical and analytical methods (such as the conformal bootstrap). The excellent local scientific environment at the Humboldt University and DESY Zeuthen, and close contacts of the PI with atomic physicists in Univeristy of Innsbruck, Austria are expected to contribute to the success of the proposed project and make a significant impact on the aforementioned fields.