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

长程相互作用量子自旋系统中的吸收态相变

• 批准号: 500475418
• 负责人: Professor Igor Lesanovsky
• 金额: --
• 依托单位: Arbeitsbereich Numerische Mathematik
• 依托单位国家: 德国
• 项目类别: Research Units
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/500475418?language=en
• 关键词: Absorbing; state; phase; transitions; long

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.

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。这涉及到它们的真实的时间演化以及它们的定态分析。解决这个问题的进展目前备受追捧，这里的突破将直接影响到最近几个物理领域的最新研究，从凝聚态物理到量子光学。该项目的目标是开发和应用一种基于树张量网络的新型数值方法来分析具有长程相互作用和吸收态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。这些都是非平衡态物理学的典型例子，它们可能显示出在已知的平衡态普适类之外的临界行为。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。我们的工作计划是这样设计的，它强烈集成了数值技术的发展，提供在非平衡相变的理解进步。具体来说，我们的数值方法是基于树张量网络结合一种新的技术，用于集成的量子主方程。这种结合可以使相变附近的临界现象的研究，而且可以允许二维系统的研究。我们的想法将首先基准对已知的非平衡过程的吸收状态，并随后应用到长程相互作用的情况下。我们的研究有望推动开放量子系统的最先进的数值方法，并可能揭示当前非平衡物理领域的开放问题，可能使我们能够发现新形式的普遍行为和新的非平衡相多体开放量子系统。