Final Report Summary - QUERG (Quantum entanglement and the renormalization group)
The project QUERG (quantum entanglement and the renormalization group) envisions the use of techniques developed in the context of quantum information theory to describe strongly correlated quantum many-body systems.
Definitive progress has been made towards getting a better understanding of the role of entanglement in such systems. This lead the possibility of describing fermionic sytems in 2 dimensions and of quantum field theories using variational real-space renormalization group methods, and both of those developments are opening up novel research areas (which is witnessed by the large number of groups worldwide starting to pursue similar research directions).
One of the highlights of the project has been the simulation of relativistic quantum field theories using a variational method – something that was believed by Feynman to be impossible. A second highlight has been the formulation of a Quantum Metropolis Algorithm – thereby generalizing the ubiquitous Metropolis algorithm to the quantum realm. This solved a big open problem in the field of quantum computation. A third highlight has been the formulation of tensor network methods for simulating 2-dimensional fermionic systems such as the Hubbard model – this has attracted a lot of attention from the condensed matter community. Finally, there has been a synergy of techniques developed in the field of differential geometry and matrix product states, leading to a completely new picture in which we can depict dispersion relations and elementary excitations /particles as object living in the so-called tangent plane of the manifold of (continuous) matrix product states.
In summary, this project has enabled us to explore the rich territory of strongly correlated quantum many-body systems with completely new tools, with entanglement as our guiding principle, and this has led to fascinating new insights into the nature of correlations in those systems.
Definitive progress has been made towards getting a better understanding of the role of entanglement in such systems. This lead the possibility of describing fermionic sytems in 2 dimensions and of quantum field theories using variational real-space renormalization group methods, and both of those developments are opening up novel research areas (which is witnessed by the large number of groups worldwide starting to pursue similar research directions).
One of the highlights of the project has been the simulation of relativistic quantum field theories using a variational method – something that was believed by Feynman to be impossible. A second highlight has been the formulation of a Quantum Metropolis Algorithm – thereby generalizing the ubiquitous Metropolis algorithm to the quantum realm. This solved a big open problem in the field of quantum computation. A third highlight has been the formulation of tensor network methods for simulating 2-dimensional fermionic systems such as the Hubbard model – this has attracted a lot of attention from the condensed matter community. Finally, there has been a synergy of techniques developed in the field of differential geometry and matrix product states, leading to a completely new picture in which we can depict dispersion relations and elementary excitations /particles as object living in the so-called tangent plane of the manifold of (continuous) matrix product states.
In summary, this project has enabled us to explore the rich territory of strongly correlated quantum many-body systems with completely new tools, with entanglement as our guiding principle, and this has led to fascinating new insights into the nature of correlations in those systems.