Ground states of quantum Hamiltonians in 1D can be very entangled

The application of DMRG to 1D quantum systems is a great success story, which we today connect to low-lying states containing little entanglement. However, as we increase the local spin dimension, quantum spin chains can have surprisingly entangled ground states, beyond log corrections to the area law. We will discuss these strange beasts that appear even for translationally invariant or unfrustrated Hamiltonian