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Wavefunctions for strongly correlated systems

Periodic Reporting for period 3 - WASCOSYS (Wavefunctions for strongly correlated systems)

Reporting period: 2017-05-01 to 2018-10-31

"Complex quantum systems which exhibit strong correlations are at the heart of many exciting phenomena and open problems in physics and beyond. In the fractional quantum Hall effect (FHQE), for instance, the electrons ""fractionalize"", giving rise to precisely quantized edge currents useful for high-precision metrology or quantum computation. Studying complex molecules, such as for drug development, crucially relies on our ability to simulate complex correlated quantum systems. And fundamental questions about the constituents of matter, such as strong confinement of quarks, yet again have complex and strongly correlated quantum systems at their root. Gaining a better understanding of these systems is thus important both from a fundamental and a technological point of view.

Yet, the same reason which makes these systems that rich also makes them extremely hard to understand: The presence of complex quantum correlations, termed ""entanglement"". Entanglement, on the other hand, has always been a central topic of study in Quantum Information Theory, where a wide range of tools for its understanding and manipulation has been developed. Thus, it is suggestive to apply quantum information concepts to enhance our understanding of complex quantum systems.

The goal of the project WASCOSYS - ""Wavefunctions for strongly correlated systems"" - is to apply tools from Quantum Information Theory to build a framework for the study of complex quantum systems, based on their entanglement structure. The central tool are so-called tensor networks: They provide the natural language to describe those systems based on the structure of their entanglement, and allow to reconcile the local structure imposed by physical interactions with the globally emergent entanglement pattern which gives rise to exotic phases. The results of the project will provide us with a whole range of new tools to study and understanding the physics of strongly correlated systems which will, in combination with experimental findings and quantum simulations, ultimately lead to new applications and materials based on strongly correlated matter.

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We have worked systematically towards building a comprehensive framework for the description of strongly correlated quantum systems based on their entanglement. To this end, we have explored several frontiers.

First, we have worked towards a full classification of the different types of global entanglement patterns, and thus different exotic states of matter, which can appear in complex quantum systems. A particular focus has been on the way how the bulk properties of a system are related to the behavior seen at its boundary, which is a key feature of quantum systems exhibiting complex entanglement patterns.

Second, we have built a comprehensive framework for the understanding of so-called topological phases and transitions between them, driven by a mechanism known as anyon condensation. In particular, we were able to show that the behavior of the bulk excitations of the system is in one-to-one correspondence with the texture of the entanglement at the boundary. This allowed us to classify these phases through the phases of their entanglement, and to devise probes which allow for a detailed study of these systems and their transitions.

Finally, we have developed a range of techniques which allow us to generalize the quantum information based description of many-body states with tensor networks to new regimes, such as so-called chiral spin liquids or systems in the continuum, and have devised ways to build new topological wavefunctions from known ones. These ideas will form starting points for the systematic construction and classification of novel phases of matter based on tensor networks in the second part of the project.
The project WASCOSYS has already led to a classification of a wide range of exotic phases based on their local properties, and we have developed the tools which will allow us to proceed further in that direction in the second half of the project, ultimately leading to a complete picture. In particular, we have made significant advances in the detailed structure of bulk-boundary correspondences in a wide range of settings, enabled by the fact that a description based on tensor networks assigns an explicit one-dimensional quantum system to the entanglement at the boundary, a property which is unique to this description. We have also devised ways to build variety of wavefunctions with novel properties, forming a starting point for further investigations.

In the second half of the project, these tools will allow us to fully classify the different topological phases found in complex quantum systems, to systematically study transitions between them, to construct and study models with novel phases such as hierarchies of topological spin liquids, gapped systems with gapless edge modes, or systems described by exotic conformal field theories, and thus to overall significantly advance our understanding of the rich and unconventional physics displayed by complex interacting quantum systems.