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

TL;DR

This paper introduces a variational method combining continuous unitary transformations and tensor networks to accurately diagonalize many-body localized Hamiltonians, capturing the full spectrum and local integrals of motion.

Contribution

It develops VCUTs, a novel approach that efficiently diagonalizes MBL Hamiltonians and tracks entanglement, extending to larger system sizes than previous methods.

Findings

Accurately reproduces the full spectrum of disordered Heisenberg chains.

Scales to 48 sites, surpassing previous size limitations.

Identifies local integrals of motion in the MBL phase.

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.