Project description
Lee-Yang theorem extends to the quantum realm to describe quantum many-body systems
Lee-Yang theory provides a description of phase transitions and analytic properties of thermodynamic functions based on the distribution of partition function zeros. Lee-Yang zeros are no longer just a theoretical concept; they have recently been determined from measurements of fluctuating observables, offering a completely new perspective on phase transitions in interacting many-body systems. The EU-funded QuLeeYang project will expand the Lee-Yang theory beyond classical equilibrium systems. It will formulate a unifying theory of phase transitions in interacting quantum many-body systems from the perspective of Lee-Yang zeros and will make use of engineered quantum devices to test the predictions about phase transitions. The project's results will have important implications for quantum information processing and quantum thermodynamics.
Objective
Over the last years, investigations of Lee-Yang zeros – complex zeros of the partition function for systems of finite size – have become an indispensable theoretical tool in equilibrium statistical physics with diverse applications, ranging from protein folding and percolation to complex networks and magnetism. In the thermodynamic limit, the Lee-Yang zeros approach the real value of the control parameter for which a phase transition occurs. Despite these developments, surprisingly little attention has so far been devoted to applications of Lee-Yang theory beyond classical equilibrium systems. One reason may be that Lee-Yang zeros (being complex values of physical quantities) for years were seen as a purely theoretical concept with little relevance to experiments. However, this view has recently been contested by several experiments, in which Lee-Yang zeros have been determined. A novel cumulant method allows for the determination of Lee-Yang zeros from measurements of fluctuating observables, thus offering a completely new perspective on phase transitions in interacting many-body systems. Here, building on this cumulant method, I propose to formulate a unifying theory of phase transitions in interacting quantum many-body systems, including space-time, dynamical, and quantum phase transitions, from the perspective of Lee-Yang zeros. I will connect this theoretical framework to large-deviation statistics, fluctuation relations, and many-body entanglement in non-classical systems. Furthermore, I will devise experimental schemes to test my predictions and, in particular, investigate quantum phase transitions in engineered quantum devices. Fulfilling these objectives will expand the field far beyond its current state-of-the-art and potentially result in major scientific breakthroughs with important implications for other research fields, such as quantum information processing and quantum thermodynamics.
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Funding Scheme
MSCA-IF - Marie Skłodowska-Curie Individual Fellowships (IF)Coordinator
02150 Espoo
Finland