Over the past few decades, the increasing ability to control and manipulate nanoscale systems has opened up a whole new world of opportunities to explore and exploit quantum physics. The overarching aim of this project was to investigate the connection between the phase-behavior of interacting many-body quantum systems, such as quantum computers, and their smaller individual constituents, such as single quantum bits (“qubits”). Besides fundamental aspects, the understanding of this connection is of great importance to predict – and design – the properties of future quantum devices that may be used to store, process, and transfer information in new ground-breaking ways.
To this end, the objective of the project was to develop a unified Lee-Yang theory to describe phase transitions in quantum many-body systems. The original Lee-Yang theory of classical equilibrium phase transitions connects the phase-behavior of large systems in the thermodynamic limit to the properties of small systems by considering the partition function zeros in the complex plane of an external control parameter. The crucial insight of Lee and Yang was that these complex zeros, with increasing system size, approach the real value of the control parameter for which a phase transition occurs in the thermodynamic limit. The main aim of the project was to develop a generalized theory for non-equilibrium quantum systems lacking a partition function.
During the five months that the project was ongoing, we found that generalized Lee-Yang zeros play an important role for predicting and describing both space-time phase transitions and dynamical phase transitions. By identifying appropriate generalized partition functions, many of the ideas and results of the Lee-Yang theory of classical equilibrium phase transitions can be extended to non-equilibrium phase transitions.
