# Pieter W. Claeys

pwclaeys@gmail.com# News

## Editors' Suggestion in Physical Review B

10 January 2020 More good news from APS: our paper on **Variational Schrieffer-Wolff transformations for quantum many-body dynamics** has been published in **Physical Review B** and chosen as **Editors' Suggestion**! It is currently highlighted on the Physical Review B homepage, with an illustration of our method: a physical model is translated to a Hamiltonian matrix, that matrix is subsequently simplified (returning an effective Hamiltonian), and we can efficiently calculate dynamics using the effective model.

In other words: *The description of nonequilibrium dynamics in interacting quantum systems is a long-standing challenge within condensed matter physics. In this theoretical work, the authors introduce a method to block-diagonalize low-energy sectors of strongly interacting Hamiltonians by variationally computing generators of rotations, equivalent to a nonperturbative dressing of quasiparticle excitations. This procedure allows for the calculation of effective dynamics including quenches and response functions, as is demonstrated in a Fermi-Hubbard model and an integrability-broken XY model, both of which demonstrate excellent convergence.*

## Cavendish Laboratory

15 November 2019 Part two of the postdoc experience: I've started a new postdoc as research associate at the **Cavendish Laboratory** at the **University of Cambridge**! I've joined the Theory of Condensed Matter group, where I will be working with Austen Lamacraft, Claudio Castelnovo, and Nigel Cooper.

## Variational Schrieffer-Wolff transformations

31 October 2019New joint work with Jonathan Wurtz and Anatoli Polkovnikov! Our paper on **Variational Schrieffer-Wolff Transformations for Quantum Many-Body Dynamics** is now available on **arXiv**.

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.*