Variational Schrieffer-Wolff transformations for quantum many-body dynamics
Claeys, Pieter W.
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Citation (published version)Jonathan Wurtz, Pieter W Claeys, Anatoli Polkovnikov. "Variational Schrieffer-Wolff transformations for quantum many-body dynamics." Physical Review B, Volume 101, Issue 1, https://doi.org/10.1103/physrevb.101.014302
Building on recent results for adiabatic gauge potentials, we propose a variational approach for computing the generator of Schrieffer-Wolff transformations. These transformations consist of block diagonalizing a Hamiltonian through a unitary rotation, which leads to effective dynamics in a computationally tractable reduced Hilbert space. The generators of these rotations are computed variationally and thus go beyond standard perturbative methods, with error controlled by the locality of the variational ansatz. The method is demonstrated on two models. First, in the attractive Fermi-Hubbard model with onsite disorder, we find indications of a lack of observable many-body localization in the thermodynamic limit due to the inevitable mixture of different spinon sectors. Second, in the low-energy sector of the XY spin model with a broken U(1) symmetry, we analyze ground-state response functions by combining the variational Schrieffer-Wolf transformation with the truncated spectrum approach.
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