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

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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.