Editors' Suggestion in Physical Review B10 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 Laboratory15 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 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.