Absorbing state phase transitions in long-range interacting quantum spin systems

理解具有长程相互作用的开放多体量子系统的动力学是物理学中最具挑战性的任务之一。这涉及到它们的实时演化以及它们的定态分析。解决这一问题的进展目前备受追捧，这里的突破将直接影响从凝聚态物理到量子光学等几个物理领域的最新研究。本项目的目标是开发和应用一种新的基于树张量网络的数值方法来分析具有长程相互作用和吸收态特征的耗散多体量子系统。在这种情况下，人们通常可以观察到所谓的吸收状态相变。这些都是非平衡物理的范例，可能显示出在已知的平衡普适性类之外的临界行为。为了实现这一雄心勃勃的目标，我们的研究团队结合了数值分析和多体量子理论的专家。我们的工作方案是这样设计的，它将数值技术的发展与在理解非平衡相变方面的进展紧密地结合在一起。具体地说，我们的数值方法是基于树张量网络和一种新的积分量子主方程的技术。这种结合可以使研究相变附近的临界现象成为可能，而且还可以研究二维系统。我们的想法将首先以已知的具有吸收状态的非平衡过程为基准，然后应用于存在远程相互作用的情况。我们的研究承诺推动开放量子系统数值方法的最新发展，并可能阐明当前非平衡物理领域的悬而未决的问题，潜在地使我们能够发现多体开放量子系统的新形式的普遍行为和新的非平衡相。

Understanding the dynamics of open many-body quantum systems with long-range interactions is one of the most challenging tasks in physics. This concerns their real time evolution as well as the analysis of their stationary state. Advances in tackling this problem are currently much sought after and breakthroughs here will impact directly on recent state-of-the-art research in across several physical domains, ranging from condensed matter physics to quantum optics. The goal of this project is to develop and apply a novel numerical approach based on tree tensor networks to the analysis of dissipative many-body quantum systems that feature long-range interactions together with an absorbing state. In such setting one can typically observe so-called absorbing state phase transitions. These are paradigmatic instances of non-equilibrium physics that may display critical behaviour lying outside that of known equilibrium universality classes. To achieve this ambitious goal, our research team combines experts from numerical analysis and many-body quantum theory. Our work programme is designed such that it strongly integrates the development of numerical techniques with delivering advances in the understanding of nonequilibrium phase transitions. Specifically, our numerical approach is based on tree tensor networks combined with a novel technique for integrating the quantum master equation. This combination may enable the study of critical phenomena near phase transitions and may moreover permit the study of two-dimensional systems. Our ideas will first be benchmarked against known nonequilibrium processes with absorbing states and subsequently applied to situations in which long-range interactions are present. Our research promises to push the state-of-the-art of numerical methods for open quantum systems and may allow to shed light on current open questions in the domain of nonequilibrium physics, potentially enabling us to uncover new forms of universal behaviour and new nonequilibrium phases of many-body open quantum systems.