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

Maxime Dupont; Nicolas Laflorencie

doi:10.1103/physrevb.99.020202

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arXiv · 1807.01313

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

Maxime Dupont·Nicolas Laflorencie

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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.

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Maxime Dupont, Nicolas Laflorencie. 2019-01-15. Many-body localization as a large family of localized ground states. https://doi.org/10.1103/physrevb.99.020202

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