Norbert Schuch

Entanglement of Complex Quantum Systems

Max Planck Institute of Quantum Optics

Hans-Kopfermann-Str. 1

85748 Garching

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The research in our group is focused at the interface between quantum information theory and strongly correlated many-body systems. Strongly correlated quantum systems exhibit a wide range of exotic physical phenomena, such as topologically ordered phases with quantized egde currents and exotic excitations, which arise from their intricate entanglement structure. At the same time, the theory of entanglement has been a core topic in quantum information theory, where a wide range of tools to classify, quantify, and utilize entanglement has been developed, suggesting to apply this toolbox to the study of strongly correlated systems.

In our group, we apply quantum information methods to the systematic study of strongly correlated systems, with three main goals: First, we aim to classify the possible phases of strongly correlated systems, this is, the distinct types of global entanglement. Second, we use these insights to study specific strongly correlated systems by means of tailored variational wavefunctions. Third, we study the fundamental limitations to our understanding of these systems imposed by quantum complexity theory.

An important tool in our study is the description of many-body states in terms of tensor networks. Tensor network states provide a description of a global wavefunction, as well as an associated Hamiltonian, from a single local tensor which encapsulates all properties of the system, and thus allow for an explanation of the global behavior of strongly correlated systems based on their local properties.

Entanglement and classification of phases of matter

Different topological phases are distinguished by the different structure of their global entanglement. We explore the different types of global entanglement, and thus the different possible phases of matter, and how their arise from the local properties of the system as imposed by its interactions. To this end, we study the different ways in which symmetries of the system, such as SU(2), can be encoded locally in the tensor network description, and the different algebraic structures these encodings give rise to, with the goal of developing a complete theory of strongly correlated phases starting from a local characterization of the system.

Variational wavefunctions for strongly correlated systems

Many important insights into strongly correlated systems have come through variational wavefunctions, such as the BCS wavefunction for superconductivity and the Laughlin state for the fractional quantum Hall effect. We use tensor network states to construct explicit variational wavefunctions for strongly correlated systems by encoding the desired structure of the interactions locally into the tensor, and subsequently study the emerging global properties such as topological order or fractionalization, and the way in which they can be controlled by the external parameters imposed on the system.

Quantum complexity of many-body systems

The richness of physical phenomena displayed by strongly correlated systems comes at the price of an increased computational difficulty of these systems. We use the tools of quantum complexity theory to study the origin of these difficulties, which on the one hand allows us to assess the fundamental limitations to our ability to simulate these systems, but at the same time, it also helps us to understand the reasons for this increased complexity, and thus to identify specific classes of systems which are accessible by classical or quantum simulations.

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