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New preprint today! 
"Localisation of Interacting Power-Law Random Banded Fermions", by S. J. Thomson and M. Schiró - https://arxiv.org/abs/2004.11844
#physics #research #quantum #manybodylocalization #postdoclife #quantumtechnology #condensedmatter #condmat #nonequilibrium #disorder
"Localisation of Interacting Power-Law Random Banded Fermions", by S. J. Thomson and M. Schiró - https://arxiv.org/abs/2004.11844 #physics #research #quantum #manybodylocalization #postdoclife #quantumtechnology #condensedmatter #condmat #nonequilibrium #disorder
In this work, we study the effects of (random) long-ranged couplings on a model of interacting fermions, and show that long-range kinetic terms lead to delocalisation (i.e. metallic behaviour), while long-range interacting terms (surprisingly!) do not. 
The question of how long-ranged couplings can affect localisation in disordered systems is still largely unanswered, with many (conflicting) works mostly relying on approximate calculations or exact numerical simulations of very small numbers of particles.
Here, we've tried to reach beyond those limitations, using a powerful new technique called the flow equation approach, in part developed by Marco Schiró and I over the last few years. (e.g. in https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.060201 and https://link.springer.com/article/10.1140/epjb/e2019-100476-3)
Since our last major work on the topic ( https://journals.aps.org/prb/abstract/10.1103/PhysRevB.97.060201), I've completely overhauled the technique, reworking it from the ground-up and rewriting almost every line of code to extend and improve it, giving us far better accuracy and efficiency than ever before. 
Along the way, we realised that the biggest downside of our technique - the generation of long-range couplings which render the model 'non-sparse' - could be a huge advantage if, indeed, what we wanted to study was a model *with* long-range couplings.
And so, this new preprint began to take shape - https://arxiv.org/abs/2004.11844 . It's been a long road - we've had the main result for over a year, but spent a long time checking many technical aspects of the calculations and figuring out where we did and did not agree with prior work.
Relatively recently, we realised that the specific physical model I chose to study is, to the best of our knowledge, entirely new and hasn't been studied by anyone else before. The main difference is that we study a *maximally random* system, unlike any other work before us.
In fact, in the truly long-ranged limit, our model becomes a modified version of the celebrated Sachdev-Ye-Kitaev (SYK) model, known to be maximally random and maximally chaotic.
As a result, our model seems to be significantly *more localised* than other long-range models studied in the literature, and escapes some of the bounds placed on other (usually non-random) models which argue that localisation is inevitably destroyed by long-range couplings.
Which brings us to our main result: long-range couplings do not necessarily spell disaster for localisation, and in fact it depends very subtly on the nature of the couplings whether they can trigger delocalisation. (We also studied many other models not shown in this work.)
[Sidebar: This turns out to be completely independent of 'long-range shielding' arguments where translationally invariant long-range couplings can engage in a co-operative screening effect to 'hide' exponentially large regions of a system over long (but finite) timescales. 
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