Construction of exact constants of motion and effective models for many-body localized systems

摘要

One of the defining features of many-body localization is the presence ofextensively many quasi-local conserved quantities. These constants of motionconstitute a corner-stone to an intuitive understanding of much of thephenomenology of many-body localized systems arising from effectiveHamiltonians. They may be seen as local magnetization operators smeared out bya quasi-local unitary. However, to accurately identify such constants of motionremains a challenging problem. Current numerical constructions often capturethe conserved operators only approximately or trade desirable properties suchas exactly commuting with the Hamiltonian against each other, restricting aconclusive understanding of many-body localization. In this work, we usemethods from the theory of quantum many-body systems out of equilibrium toestablish a new approach for finding a complete set of exact constants ofmotion which are in addition guaranteed to represent Pauli-z operators. By thiswe are able to construct and investigate the proposed effective Hamiltonianusing exact diagonalization. Hence, our work provides an important toolexpected to further boost inquiries into the breakdown of transport due toquenched disorder. We end with devising extensions to tensor network methods.