A renormalization group approach to identifying the local quantum numbers in a many-body localized system

Many-body localization is a dynamical phase of matter that is characterized by the absence of thermalization. One of the key characteristics of many-body localized systems is the emergence of a large (possibly maximal) number of local integrals of motion (local quantum numbers) and corresponding conserved quantities. We formulate a robust algorithm for identifying these conserved quantities, based on Wegner’s flow equations – a form of the renormalization group that works by disentangling the degrees of freedom of the system as opposed to integrating them out. We test our algorithm by explicit numerical comparison with more engineering based algorithms – Jacobi rotations and bi-partite matching. We find that the Wegner flow algorithm indeed produces the more local conserved quantities and is therefore more optimal. A preliminary analysis of the conserved quantities produced by the Wegner flow algorithm reveals the existence of at least two different localization lengthscales.