Flow Equations for MBL

This is just a short post to advertise our new pre-print that appeared on arXiv this morning: “Time Evolution in Many-Body Localized Phases with the Flow Equation Approach”.

I’ll save the full write-up of it until the paper is properly published: for my non-academic readers, let me just be clear up front that this is a pre-print, which means that it hasn’t yet been published by a journal or gone through the peer-review process.

Standard practice in physics is that we upload new papers to arXiv (pronounced ‘archive’, as in the Greek letter ‘chi’) at roughly the same time as we submit them to a journal for peer review. The idea is that in doing so, we i) make the papers available for free without readers needing to pay a journal subscription charge, and ii) we make the work available to the community instantly without needing to wait for months in peer review. This means people can build on (or attempt to refute) our work before it’s ‘properly’ published, which allows the entire field to progress faster. Pre-prints have been the done thing in physics for as long as I’ve been in the game, and in the last few years other fields have rapidly begun adopting them too (e.g. bioRxiv).

When reading an arXiv paper that hasn’t yet been peer-reviewed and published by a reputable journal, I’d encourage you to exercise caution and critical thinking and not just accept its results at face value – essentially, you should be reviewing it as you read it. (It almost goes without saying that this should also be how you approach papers published in reputable journals too, but at least there you hope that the peer review process should have eliminated any real howling errors – with arXiv, you shouldn’t even make that assumption.)

Frankly, this is a distinction that I wish some science journalists would pay more attention to – a lot of the overly-excited “Einstein Was Wrong And You Won’t Believe What Happened Next!” style of popular science articles are based around arXiv papers which end up not meeting the standards of rigorous science and either never get published or end up in fringe journals.

Anyway – with that out of the way, let me say a few words about our new paper. It’s the first paper from my postdoc, representing around 9 months of work. In it, we develop a new technique to examine many-body localisation (MBL), and in particular we use it to calculate how an MBL system evolves in time, which hasn’t been studied much using existing methods.

The method we propose allows studies of much larger numbers of particles than most numerical (i.e. computational) techniques, and is more directly connected to microscopic models than many of the analytical (i.e. pen and paper) treatments out there – essentially, the method we’ve used bridges the gap between these two principal avenues of investigation into many-body localisation, allowing us to test some previous assumptions about the behaviour of these systems and enabling new lines of investigation that aren’t possible/practical with other methods. In this work we’ve taken the first steps along this road, but there’s a lot more than can be done with the methods we’ve developed here.

There’s also a lengthy supplementary material file posted along with the paper, in which we flesh out some of the behind-the-scenes mechanics of the calculation. This is largely standalone and separate from the new results in the main paper, but may be useful for people who wish to understand our technique in more detail (just be thankful that I didn’t include the page-long equations that were in an earlier draft…). Here, we calculate various known quantities to see how our method compares with other existing methods – in short, it compares pretty well. It breaks down if you try to apply it to a metallic phase of matter, but for the many-body (or even single-body) localised phases which we’re interested in, it works very well indeed, reproduces known results and furthermore allows us to do calculations that, to the best of my knowledge, no other method currently can.

If any of that piques your interest, please do read and share our work. We’d welcome any feedback, comments, criticism and suggestions for future calculations using this method. In the meantime, keep your fingers crossed for a smooth, constructive and quick peer-review process – expect a more thorough blog post on the topic of the paper once it’s published for real!