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

Abstract

Many-body localization (MBL) addresses the absence of thermalization in interacting quantum systems, with non-ergodic high-energy eigenstates behaving as ground states, only area-law entangled. However, computing highly excited many-body eigenstates using exact methods is very challenging. Instead, we show that one can address high-energy MBL physics using ground-state methods, which are much more amenable to many efficient algorithms. We find that a localized many-body ground state of a given interacting disordered Hamiltonian ${\mathcal{H}}_0$ is a very good approximation for a high-energy eigenstate of a parent Hamiltonian, close to ${\mathcal{H}}_0$ but more disordered. This construction relies on computing the covariance matrix, easily achieved using density-matrix renormalization group for disordered Heisenberg chains up to $L=256$ sites.

6 pages, 4 figures, supplemental material included (2 pages, 3 figures)

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• From eigenstate to Hamiltonian: Prospects for ergodicity and localization
• Parent Hamiltonian Reconstruction of Jastrow-Gutzwiller Wavefunctions
• Emergent dimerization and localization in disordered quantum chains
• A stabilization mechanism for many-body localization in two dimensions
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• Dirty bosons on the Cayley tree: Bose-Einstein condensation versus ergodicity breaking
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• Engineering many-body quantum Hamiltonians with non-ergodic properties using quantum Monte Carlo
• From Bose glass to many-body localization in a one-dimensional disordered Bose gas