Many-body localization (MBL) is currently an intensely studied topic and characterized by the fact that certain strongly disordered systems fail to thermalize. For sufficiently strong disorder in one dimension, all eigenstates of MBL systems fulfill the area law of entanglement.
The generalization of Matrix Product States (MPS) to continuous systems, as proposed in Phys. Rev. Lett. 104, 190405(2010), provides a powerful variational ansatz for the ground state of strongly interacting quantum field theories in one spatial dimension.