Variational Schrieffer-Wolff Transformations for Quantum Many-Body Dynamics

TL;DR

This paper introduces a variational method to compute Schrieffer-Wolff transformations for quantum many-body systems, enabling effective dynamics analysis beyond perturbation theory with controlled errors.

Contribution

It develops a variational approach for Schrieffer-Wolff transformations that improves upon standard methods by controlling errors via the variational ansatz's locality.

Findings

Indications of a lack of observable many-body localization in the disordered Fermi-Hubbard model.

Analysis of ground state response functions in the XY spin model with broken U(1)-symmetry.

Demonstration of the method on two quantum models with insights into their dynamics.

Abstract

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 generator of these rotations are computed variationally and thus go beyond standard perturbative methods; the error is controlled by the locality of the variational ansatz. The method is demonstrated on two models. First, in the attractive Fermi-Hubbard model with on-site 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 SW transformation with the truncated spectrum approach.