Exact projector Hamiltonian, local integrals of motion, and many-body localization with topological order

Abstract

In this work, we construct an exact projector Hamiltonian with interactions, which is given by a sum of mutually commuting operators called stabilizers. The model is based on the recently studied Creutz-ladder of fermions, in which flat-band structure and strong localization are realized. These stabilizers are local integrals of motion from which many-body localization (MBL) is realized. All energy eigenstates are explicitly obtained even in the presence of local disorders. All states are MBL states, that is, this system is a full many-body localized (FMBL) system. We show that this system has a topological order and stable gapless edge modes exist under the open boundary condition. By the numerical study, we investigate stability of the FMBL and topological order.

arXiv comment11 pages, 5 figures, accepted for publication in Phys. Rev. B

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• Quantum Caging in Interacting Many-Body All-Bands-Flat Lattices
• Interaction induced doublons and embedded topological subspace in a complete flat-band system
• Non-thermalized Dynamics of Flat-Band Many-Body Localization
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• Topological inverse Anderson insulator
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• Deformation of localized states and state transitions in systems of randomly hopping interacting fermions
• Flat-band full localization and symmetry-protected topological phase on bilayer lattice systems
• Localization and slow-thermalization in a cluster spin model
• Heat percolation in many-body flatband localizing systems