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

Qiyu Liu1,*, Jan-Niklas Herre2, Dante M. Kennes2,3,†, and Christoph Karrasch1,‡

  • *Contact author: qiyu.liu@tu-braunschweig.de
  • †Contact author: dante.kennes@rwth-aachen.de
  • ‡Contact author: c.karrasch@tu-braunschweig.de
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Phys. Rev. B 114, 094203 – Published 17 August, 2026

DOI: https://doi.org/10.1103/q4n3-r8n5

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 reproduce the full spectrum across the ergodic-to-MBL crossover at small system sizes and scale 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.

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Phys. Rev. B 114, 094203– Published 17 August, 2026
  • Received 19 March 2026
  • Revised 1 July 2026
  • Accepted 3 August 2026
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