Abstract
This paper addresses the so-called inverse problem which consists in searching for (possibly multiple) parent target Hamiltonian(s), given a single quantum state as input. Starting from , an eigenstate of a given local Hamiltonian , we ask whether or not there exists another parent Hamiltonian for , with the same local form as . Focusing on one-dimensional quantum disordered systems, we extend the recent results obtained for Bose-glass ground states [M. Dupont and N. Laflorencie, Phys. Rev. B 99, 020202(R) (2019)] to Anderson localization, and the many-body localization (MBL) physics occurring at high energy. We generically find that any localized eigenstate is a very good approximation for an eigenstate of a distinct parent Hamiltonian, with an energy variance vanishing as a power law of system size . This decay is microscopically related to a chain-breaking mechanism, also signaled by bottlenecks of vanishing entanglement entropy. A similar phenomenology is observed for both Anderson and MBL. In contrast, delocalized ergodic many-body eigenstates uniquely encode the Hamiltonian in the sense that remains finite at the thermodynamic limit, i.e., . As a direct consequence, the ergodic-MBL transition can be very well captured from the scaling of .
8 More- Received 31 July 2019
DOI:https://doi.org/10.1103/PhysRevB.100.134201
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