Pieter W. Claeys



Constructing dual-unitary gates

09 September 2020

Some follow-up work on dual-unitary circuits now on arXiv! Given a dual-unitary gate, we know exactly how to calculate its dynamical properties and we can classify all dynamics. However, so far it wasn't possible to systematically construct dual-unitary gates, such that most works were restricted to qubit systems or Hadamard gates. In the paper, titled Ergodic and non-ergodic dual-unitary quantum circuits with arbitrary local Hilbert space dimension, we (perhaps not surprisingly) show how to construct dual-unitary gates for any dimension of the local Hilbert space with any desired level of ergodicity. We then also show how such systems relax to either an infinite-temperature Gibbs state or a generalized Gibbs ensemble, with an additional example on prethermalization. Joint work with Austen Lamacraft.

Dual-unitary quantum circuits can be used to construct 1+1 dimensional lattice models for which dynamical correlations of local observables can be explicitly calculated. We show how to analytically construct classes of dual-unitary circuits with any desired level of (non-)ergodicity for any dimension of the local Hilbert space, and present analytical results for thermalization to an infinite-temperature Gibbs state (ergodic) and a generalized Gibbs ensemble (non-ergodic). It is shown how a tunable ergodicity-inducing perturbation can be added to a non-ergodic circuit without breaking dual-unitarity, leading to the appearance of prethermalization plateaux for local observables.

Quantum Fluids in Isolation

04 September 2020

Catch my recent seminar on Joshuah Heath's Quantum Fluids in Isolation virtual seminar series, where I talked and gesticulated about recent results on Thermalization and scrambling in dual-unitary circuit models. It was a fun experience, and I was glad to be part of such an interesting seminar series — do check out the upcoming and previous talks on the website.

Quantum lattice models with time evolution governed by local unitary quantum circuits can serve as a minimal model for the study of general unitary dynamics governed by local interactions. Although such circuit dynamics exhibit many of the features expected of generic many-body dynamics, exact results generally require the presence of randomness in the circuit. After a short introduction to general unitary circuit models, we discuss the class of dual-unitary circuits characterized by an underlying space-time symmetry. We show how in these models exact results can be obtained and related for the thermalization of correlations and the scrambling of out-of-time-order correlators.

Integrability and dark states in central spin models

28 August 2020

Our paper on Integrability and dark states in an anisotropic central spin model is now published in Physical Review Research as a Rapid Communication! My first last-author paper, and joint work with Tamiro Villazon and Anushya Chandran.

A key image and blurb are also highlighted on the PRResearch homepage.