Among the most defining events in physics during the last decades were the spectacular advances made in the field of quantum many-body systems: the observation of quantum phase transitions in optical lattices, the creation of long-range entanglement and the realization that many-body quantum correlations can be used to build quantum computers are only
a few of the remarkable breakthroughs. The description and simulation of such strongly correlated quantum systems and their associated entanglement structure represent some of the biggest challenges and opportunities in theoretical physics, and the investigation of those topics forms the central objective of this proposal.
Our main body of research is concerned with the description of the relevant wavefunctions of quantum many-body systems. The identification and quantification of the precise quantum correlations present in those wavefunctions has opened up the possibility for formulating variational classes of wavefunctions that capture all the relevant physics needed for describing them, which will allow to simulate quantum many-body systems that cannot be simulated with other methods due to e.g. the sign problem. We will address and reformulate problems in the fields of quantum magnetism, quantum chemistry and quantum field theory, and develop novel algorithms for simulating those systems in the regimes where strong quantum correlations are present. Related issues on the topics of quantum computation, computational complexity and mathematical physics will also be explored.
We are confident that this work will impact the way we understand, observe and manipulate the quantum world. This is especially relevant since quantum effects will play an increasingly dominant role in future technologies, and success of future miniaturization efforts will crucially depend on our ability to deal with them.