Title: Behavior of l-bits near the many-body localization transition,
Abstract: Eigenstates of fully many-body localized (FMBL) systems are described by
quasilocal operators $\tau_i^z$ (l-bits), which are conserved exactly under
Hamiltonian time evolution. The algebra of the operators $\tau_i^z$ and
$\tau_i^x$ associated with l-bits ($\boldsymbol{\tau}_i$) completely defines
the eigenstates and the matrix elements of local operators between eigenstates
at all energies. We develop a non-perturbative construction of the full set of
l-bit algebras in the many-body localized phase for the canonical model of MBL.
Our algorithm to construct the Pauli-algebra of l-bits combines exact
diagonalization and a tensor network algorithm developed for efficient
diagonalization of large FMBL Hamiltonians. The distribution of localization
lengths of the l-bits is evaluated in the MBL phase and used to characterize
the MBL-to-thermal transition.