I study how quantum entanglement in many-body systems can give rise to collective phenomena which have no classical analogue, such as topological phases of matter or quantum criticality. To this end, I like to use a combination of tools, including numerics (e.g., tensor network methods) and analytics (e.g., field theory or solvable lattice models). I am also excited by the prospect of realizing such exotic phenomena in engineered cold atom quantum simulators, which can probe regimes inaccessible by numerical and analytical tools