Entanglement scaling and criticality with tensor networks

Computer simulations of matter in which quantum particles strongly interact with one another are essential for progress in understanding exotic systems such as quantum spin liquids , strongly correlated electrons, ultracold atoms in optical lattices, and topological matter. Because of the complexity of the computational problems, it is essential to develop efficient numerical techniques. In this research project we plan to develop new schemes to extend existing numerical techniques based on tensor networks, and to lift them to new levels of precision. The central idea is to use a renormalization-group parametrization based on the entanglement entropy. Our analysis and new framework will enable future progress on a broad range of questions of current interest, such as the nature of spin liquids in various frustrated quantum magnets, quantum criticality in one- and two-dimensional quantum many body systems and conformal field theories in three space-time dimensions.

Computer simulations of matter in which quantum particles strongly interact with one another are essential for progress in understanding exotic systems such as quantum spin liquids, strongly correlated electrons, ultracold atoms in optical lattices, and topological matter. Because of the complexity of the computational problems, it is essential to develop efficient numerical techniques. In this research project we plan to develop new schemes to extend existing numerical techniques based on tensor networks, and to lift them to new levels of precision. The central idea is to use a renormalization-group parametrization based on the entanglement entropy. Our analysis and new framework will enable future progress on a broad range of questions of current interest, such as the nature of spin liquids in various frustrated quantum magnets, quantum criticality in one- and two-dimensional quantum many body systems and conformal field theories in three space-time dimensions.