Major themes for my research revolve around non-equilibrium phenomena in many-body systems ranging from ultra-cold atoms to strongly correlated electron materials. Specifically, I am interested in:

• Understanding the nature of entanglement, correlations and quantum mutual information in ground states and thermal states of commonly encountered many-body systems. Such properties have striking and deep connections to the classical simulability of quantum systems.
• Exploiting and further developing sophisticated tensor network theory techniques for efficiently simulating many-body quantum systems. Currently this most prominently includes the density matrix renormalization group (DMRG) method and its generalization to time-dependent phenomena via the time-evolving block decimation (TEBD) algorithm applicable to 1D systems. A major long term effort to extend the success of these methods to 2D quantum systems is underway.
• Developing a comprehensive and highly optimised freely available open-source software library for tensor network theory algorithms which can be found at www.tensornetworktheory.org.
• Connecting tensor network theory to enahnce other extremely successful techniques in condensed matter physics, such as variational Monte Carlo and dynamical mean-field theory.
• Applying these toolbox of methods to strongly driven systems to determine how its properties can be controlled on ultra-short timescales, and on longer timescales if it can be stably pushed into new phases not accessible thermally.
• Exploring foundational issues regarding quantum theory including non-locality and quantifying quantumness, as well as connections to thermodynamics of small systems and fluctuation relations.