Many-body localization as a large family of localized ground states

It is well-known that Many-Body Localized (MBL) eigenstates are only area-law entangled, even at high energy, although it is the usual hallmark of ground states of short-range Hamiltonians. It is therefore legitimate to ask whether zero-temperature physics may have some connections with MBL states. Building on this simple idea, we ask whether an arbitrary MBL state could also be the ground state of another Hamiltonian? This question falls in the more general following problem: given a single eigenstate, does it uniquely encode the underlying Hamiltonian? Using large scale DMRG simulations [1], we show that in the presence of disorder, a localized ground state is a very good approximation for an MBL excited state of a different Hamiltonian that differs only by its local disorder configuration. Following similar ideas, we also investigate [2] the ergodic - MBL transition at high energy using standard shift-invert exact diagonalization techniques.

[1] M. Dupont and N. Laflorencie, arXiv:1807.01313
[2] M. Dupont, N. Macé and N. Laflorencie, in preparation