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arXiv · 2603.12851

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

Qiyu Liu·Jan-Niklas Herre·Dante M. Kennes·Christoph Karrasch
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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.

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Qiyu Liu, Jan-Niklas Herre, Dante M. Kennes, Christoph Karrasch. 2026-03-13. Continuous unitary transformations using tensor network representations access the full many-body localized spectrum. https://arxiv.org/abs/2603.12851

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