Variational Schrieffer-Wolff transformations31 October 2019
In this paper, we propose a new method for simulating the dynamics of quantum systems. This is generally a hard problem because of the massive number of equations needing to be solved, and we show how this can be simplified by finding effective models for parts of the system. This leads to a large reduction in the number of equations, at the cost of leading to more involved models, and allowed us to get surprisingly accurate results for quantum systems with 18 (Fermi-Hubbard model) and 144 sites (integrability-broken XY spin model). We used this method to describe effects such as the (dis-)appearance of localization and correlation spreading out in a one-dimensional lattice, as in the figure below, leading to some interesting results!
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; 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.
Editors' Suggestion in Physical Review Letters30 August 2019
Our paper on counterdiabatic driving in quantum many-body systems has been published in Physical Review Letters and chosen as Editors' Suggestion! Our work is currently highlighted on the Physical Review Letters homepage and according to the website: Our Suggestions will be based on the potential interest in the results presented and, importantly, on the success of the paper in communicating its message, in particular to readers from other fields. Thanks to everyone involved!
Visiting UNB26 August 2019
This week I'll be visiting the University of New Brunswick in Canada, visiting the De Baerdemacker group and talking to a crowd of unexpecting chemists about transitionless driving in quantum many-body systems.