QuLeeYang · Lee-Yang theory of phase transitions in interacting quantum many-body systems
Horizon 2020 — Marie Skłodowska-Curie Actions
- Duration
- 2020-04-01 → 2022-03-31
- EU contribution
- €190,681
- Participants
- 1
- Scheme
- MSCA-IF
Lines connect the coordinator with its partners.
Results in brief
Lee-Yang theory of phase transitions in interacting quantum many-body systems
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.
Data: CORDIS, © European Union
Project 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.
Original text from CORDIS.
Participants
- AALTO KORKEAKOULUSAATIO SR · EspooCoordinatorFinland
Links
- View on CORDIS
- DOI: 10.3030/892956
- https://www.aalto.fi/en/department-of-applied-physics/quantum-transport-qt
Data: CORDIS, © European Union