Continuous unitary transformations using tensor network representations access the full many-body localized spectrum

Abstract: We develop variational continuous unitary transformations (VCUTs), which integrate Wegner-Wilson flow equations with tensor network techniques to approximately diagonalize many-body localized (MBL) Hamiltonians. The diagonalizing unitary is represented as a matrix product operator whose bond dimension controls the accuracy. For the disordered Heisenberg chain, VCUTs accurately reproduces the full spectrum across the ergodic-to-MBL crossover at small system sizes and scales to $L = 48$ sites. Beyond eigenenergies, the method can track the spatial entanglement structure of the diagonalizing unitary $U(l)$ at each flow step, enabling identification of local integrals of motion deep in the MBL phase.