Pieter W. Claeys



Random Matrix Theory seminar in Oxford

26 April 2022

Spent an enjoyable two days in Oxford, this time giving an introduction to Emergent random matrix behaviour in dual-unitary circuit dynamics at the Mathematical Institute! This talk was part of a series of Random Matrix Theory Seminars at the group of John Keating.

APS March Meeting

18 March 2022

I will be presenting our research on spin transport in noisy spin chains at the APS March Meeting in Chicago! Catch me at the session on Anomalous Transport of Low-Dimensional Systems, which I will also be chairing.

Also, this year's logo might look familiar! Part of the logo is taken from our Phys. Rev. Research paper on Adiabatic landscape and optimal paths in ergodic systems.

Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics

28 February 2022

New preprint on Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics on arXiv today! With Austen Lamacraft we explore the notion of emergent quantum state designs following projective measurements after a quantum quench, and investigate the importance of the dual-unitarity of the underlying dynamics. It is shown that dual-unitarity itself does not suffice to lead to an emergent quantum state design, except in the case of "solvable measurement schemes". We introduce various such schemes for different classes of dual-unitary circuits and verify our results using matrix product state calculations. These constructions are based on the recent connection between dual-unitarity and biunitarity, allowing us to incorporate complex Hadamard matrices and unitary error bases in the toolbox of dual-unitarity.

Recent works have investigated the emergence of a new kind of random matrix behaviour in unitary dynamics following a quantum quench. Starting from a time-evolved state, an ensemble of pure states supported on a small subsystem can be generated by performing projective measurements on the remainder of the system, leading to a projected ensemble. In chaotic quantum systems it was conjectured that such projected ensembles become indistinguishable from the uniform Haar-random ensemble and lead to a quantum state design. Exact results were recently presented by Ho and Choi [Phys. Rev. Lett. 128, 060601 (2022)] for the kicked Ising model at the self-dual point. We provide an alternative construction that can be extended to general chaotic dual-unitary circuits with solvable initial states and measurements, highlighting the role of the underlying dual-unitarity and further showing how dual-unitary circuit models exhibit both exact solvability and random matrix behaviour. Building on results from biunitary connections, we show how complex Hadamard matrices and unitary error bases both lead to solvable measurement schemes.