Pieter W. Claeys

pwclaeys@gmail.com

News

Talks and workshops

08 November 2021

Some news on various talks:

  • This Wednesday and Thursday I will be presenting at and participating in the virtual workshop on Spacetime Duality in Quantum Circuits organized by Suhail Ahmad Rather, Aravinda S. and Arul Lakshminarayan.

    As written on the website: The general notions of duality and symmetry act as powerful tools in understanding many-body classical or quantum systems. A particular type of duality, dubbed spacetime duality, due to the interchange of the roles of space and time, has been recently applied to locally interacting quantum lattice models and offers remarkable advantages and insights. These include building solvable models of many-body quantum chaos, toy models of many-body non-unitary dynamics, dynamical phase transitions and quantum computation. The roots of the duality lie in quantum information theory and the notions of operator entanglement, entangling power, multipartite entangled states, and quantum designs play a central role. This focus workshop will bring together some of the pioneers in the area and will highlight recent progress and future directions in such spacetime dual models. It is an activity of the Center for Quantum Information Theory of Matter and Spacetime, IIT Madras, and the Department of Physics, IIT Tirupati.

  • My talk on our recent work on the Absence of superdiffusion in certain random spin models at the Leeds-Loughborough-Nottingham seminar series is now available on YouTube.

  • Last but not least, this Friday I will be presenting some of our work on dual-unitary circuits at the mini-workshop organized to celebrate the 50th birthday of Jean-Sébastien Caux!

Leeds-Loughborough-Nottingham seminar

20 October 2021

I will be presenting our recent preprint on the Absence of superdiffusion in certain random spin models in the Leeds-Loughborough-Nottingham seminar series on Wednesday 3rd of November, 3pm UK time. This online seminar series is run by the Universities of Leeds (Dr. Papic), Loughborough (Dr. Lazarides) and Nottingham (Prof. Garrahan), with weekly seminars focusing on non-equilibrium physics. More info, including a Zoom link and recordings of previous talks, can be found on the seminar series website.

Abstract.The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian SU(2) symmetry as well as integrability, but the associated methods cannot be readily applied when integrability is broken. After an introduction to superdiffusion I will examine spin transport in such a spin-1/2 chain in which the exchange couplings fluctuate in space and time, breaking integrability but not spin symmetry, showing that operator dynamics in the strong noise limit can be analyzed using conventional perturbation theory. I will argue that the spin dynamics undergo enhanced diffusion with some interesting transient behavior rather than superdiffusion, comparing the dynamics with both a hydrodynamic approach and tensor network simulations.

Absence of superdiffusion in certain random spin models

15 October 2021

New preprint on Absence of superdiffusion in certain random spin models on arXiv today! With Austen Lamacraft and Jonah Herzog-Arbeitman we investigate the fate of superdiffusion in a Heisenberg model with noisy exchange coupling. If you would like the paper explained to you, Austen recently gave a talk at KITP that remains available to watch here.

Even though quantum dynamics is a complicated problem, the large-scale dynamics can usually be understood in terms of a few simple types of motion, including diffusion and sound waves, with the number and nature of these modes determined by conservation laws. In the simplest case of a single conservation law, diffusion of the conserved quantity is the norm — the complicated quantum system essentially undergoes a random walk. This simple picture applies even in the case of a multi-component conserved quantity such as the spin density in an isotropic paramagnet: within linear response each component diffuses separately. An exception to this phenomenology has recently attracted a lot of attention: in the one-dimensional spin-1/2 Heisenberg model, spin dynamics were found to behave superdiffusively. Spin dynamics occur faster than diffusion, in a way characteristic of the Kardar–Parisi–Zhang universality class. It is currently believed that superdiffusion arises through the combination of nonabelian symmetry and integrability. However, a fully microscopic calculation of the KPZ scaling function for any model is still lacking.

In this work we propose such a microscopic model for a Heisenberg model with a noisy exchange coupling — breaking integrability but preserving total spin symmetry. In this model, different approaches have predicted either (a weaker form of) superdiffusion or regular diffusion with small corrections. In this work we introduce a graphical picture for spin dynamics that holds near the strong noise limit. Noise causes the spin components to diffuse independently, and the Heisenberg terms introduce an interaction where spin components can either split or merge with some probability set by the interaction strength. Such a model can then be tackled using conventional tools. We find that the diffusion constant does grow in time, but that this is only a transient phenomenon: regular diffusion persists at long times, albeit with an enhanced diffusion constant. We were able to get analytic predictions for both the diffusion constant and the correlation profile, and these are in excellent agreement with numerical simulations using tensor networks. Our findings are consistent with the hydrodynamic prediction of regular diffusion with subleading corrections, and indicate the absence of superdiffusion in this class of random spin models.

The dynamics of spin at finite temperature in the spin-1/2 Heisenberg chain was found to be superdiffusive in numerous recent numerical and experimental studies. Theoretical approaches to this problem have emphasized the role of nonabelian SU(2) symmetry as well as integrability but the associated methods cannot be readily applied when integrability is broken. We examine spin transport in a spin-1/2 chain in which the exchange couplings fluctuate in space and time around a nonzero mean J, a model introduced by De Nardis et al. [Phys. Rev. Lett. 127, 057201 (2021)]. We show that operator dynamics in the strong noise limit at infinite temperature can be analyzed using conventional perturbation theory as an expansion in J. We find that regular diffusion persists at long times, albeit with an enhanced diffusion constant. The finite time spin dynamics is analyzed and compared with matrix product operator simulations.