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

MPG.PuRe (Max Planck Society)

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.

Authors 4

1. Qiyu Liu

   Technische Universität Braunschweig

   Affiliation as printed

   Technische Universität Braunschweig , Institut für Mathematische Physik , Mendelssohnstraße 3 , 38106 Braunschweig , Germany

2. Jan-Niklas Herre Aachen Institute for Theory of Statistical Physics

   RWTH Aachen University

   Affiliation as printed

   Institute for Theory of Statistical Physics , RWTH Aachen University

3. Dante Marvin Kennes
4. Christoph Karrasch

   Technische Universität Braunschweig

   Affiliation as printed

   Technische Universität Braunschweig , Institut für Mathematische Physik , Mendelssohnstraße 3 , 38106 Braunschweig , Germany