# View from the arXiv: May 2 - May 6 2022

A summary of new preprints appearing on arXiv during the week of May 2nd to May 6th 2022

Welcome to ‘View from the arXiv’, where each week I’ll put together a short list of new preprints which have appeared on arxiv.org during the week which I’ve found interesting. I’ll focus on the categories ‘*Disordered Systems and Neural Networks*’, ‘*Quantum Gases*’ and ‘*Strongly Correlated Electrons*’, and in particular the first two as these are the main areas of the arXiv which I follow. This is an entirely subjective list of things which appeal to me, and of course there are far too many interesting papers to be able cover all of them so I just choose one or two from each day to highlight here. As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details. (And let’s face it, this caveat should be applied to any published work too…!)

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**May 2nd**

*Critical localization with Van der Waals interactions, by Rahul Nandkishore*: Many-body localisation (MBL) is generally believed to be a fairly fragile quantum property of disordered systems, easily destroyed by coupling to an environment or long-range couplings within the system of interest. This work suggests that localisation in systems with a certain type of long-range interactions is perturbatively stable, i.e. while it’s not *provably* stable forever, any processes which will destroy localisation are quite weak and will only play a role over relatively long timescales, allowing us to essentially pretend that the system is localised so long as we only care about short timescales. This work also includes some estimates of effects that could cause delocalisation and their associated timescales. It’s nice to see the question of localisation in long-range systems getting some attention, as this is historically a very difficult question and there haven’t been a whole lot of attempts to answer it.

*Stabilizing Gauge Theories in Quantum Simulators: A Brief Review, by Jad C. Halimeh, and Philipp Hauke*: Quantum simulation is a hugely active field with many applications, and it’s something I’m most familiar with from the point of view of using quantum systems to simulate other condensed matter systems, but it’s much more widely applicable than that. One fascinating possibly that has arisen recently is the use of quantum simulators to realise gauge theories, which are perhaps more familiar in the context of high-energy physics than condensed matter. This brief review surveys recent developments on the use of quantum simulators to investigate gauge theories, motivated not just by the aim of investigating high-energy physics, but also the idea of investigating novel physics in unusual condensed matter systems that haven’t had a lot of attention. The bit that catches my eye in particular is the idea that disorder-free localisation can be stabilised by gauge protection, and I’d love to investigate aspects of this further in the future!

**May 3rd**

*Nonergodic delocalized paramagnetic states in quantum neural networks, by Shuohang Wu, and Zi Cai*: The title of the paper mentions neural networks, but in my language this work studies a quantum spin glass, and is another one of a relatively small number of works investigating the interplay between glassiness and quantum fluctuations, here motivated by the applications of the Hopfield neural network model in quantum information processing. The authors find that, similarly to work on other quantum spin glasses, there exist a set of states which are not ergodic (i.e. don’t thermalise, as a generic state would be expected to) but also are not many-body localised (which is believed to be impossible in a system with all-to-all couplings, as it essentially has no spatial structrue). It’s always interesting to see works exploring this challenging regime, and particularly from a different point of view than I often see with more of an emphasis on quantum information than statistical mechanics or dynamical properties, though as a follow-up work I’d like to see some dynamics to better understand how these non-ergodic extended states behave.

*Fermionic correlation functions from randomized measurements in programmable atomic quantum devices, by Piero Naldesi, Andreas Elben, Anna Minguzzi, David Clément, Peter Zoller, and Benoît Vermersch*: I have to be honest, I don’t understand random measurement schemes or what they’re used for (despite many of my colleagues working on them…!), so it was interesting to see a paper applying such a scheme to a problem I’m a bit more familiar with. A lot of what we do in the field of ultracold atoms involves relating physical properties to quantities known as correlation functions, and having good ways to accurately measure these correlation functions in experiments allows us to get detailed information about the physical systems we’re interested in. This work propoes a way to use random measurement protocols to reconstruct two-point and four-point fermionic correlation functions, which I think can already be done in ultracold atomic gases but crucially *not* on fermionic quantum processors, so developing these measurement schemes is quite important for future quantum devices. A quite technical work, perhaps, but an interesting one.

**May 4th**

*Tunable Non-equilibrium Phase Transitions between Spatial and Temporal Order through Dissipation, by Zhao Zhang, Davide Dreon, Tilman Esslinger, Dieter Jaksch, Berislav Buca, and Tobias Donner*: Materials which have crystalline order in space are all around us, have been studied for an extremely long time, and are continuing to be studied all around the world as we speak. Materials with crystalline order in *time*, however, are much newer and rarer and still hold a great deal of secrets which are yet to be fully understood. This work combines both, and investigates how an ultracold atomic gas far from equilibrium can be persuaded to transition between a phase with spatial order and a phase with spatio-temporal order, through a combination of drive and dissipation. This is very intriguing as it’s a genuinely far-from-equilibrium phenomenon that’s quite different to anything else I’ve seen studied, and might open a new line of investigation into spatio-temporal phase transitions. Spatio-temporal universality classes, anyone? (I note with interest that the authors don’t use the phrase ’time crystal’ to describe their work…!)

**May 5th**

*On Circuit Depth Scaling For Quantum Approximate Optimization, by V. Akshay, H. Philathong, E. Campos, D. Rabinovich, I. Zacharov, Xiao-Ming Zhang, and J. Biamonte*: This work looks at the quantum approximate optimisation algorithm, affectionately known as QAOA (it kind of rhymes with ‘koala’…), and in particular looks at an effect called circuit depth scaling. QAOA is an algorithm used to solve optimisation problems on current and near-future quantum hardware, and it works by applying operations known as gates to construct something called a quantum circuit. The problem is that current hardware can only apply a certain number of gates (known as the circuit depth) before the results can no longer be trusted, and so a big challenge is understanding how well variational algorithms perform when limited to a smaller circuit depth than we might ideally have. This work is an important step towards better understanding both QAOA and how it performs on the hardware we’re likely to have available in the foreseeable future.

*Dynamical mean-field theory: from ecosystems to reaction networks, by Eric De Giuli, and Camille Scalliet*: This is just a very quick one as I can’t even pretend to be able to judge the science behind this paper, but it’s an attempt to apply dynamical mean-field theory – more commonly used to understand strongly-correlated electrons and other such quantum problems – to understand biological and ecological systems. It’s fascinating to see tools from condensed matter be applied to other complex systems like this.

*Logarithmic negativity in out-of-equilibrium open free-fermion chains: An exactly solvable case, by Vincenzo Alba, and Federico Carollo*: Being able to distinguish quantum correlations from classical correlations isn’t easy, and often it’s desirable to have more finely-grained tools than standard quantities such as the von Neumann or Rényi entanglement entropies which are frequently computed in the literature. This work examines a quantity known as the logarithmic negativity, a sensitive entanglement measure, and explains how it relates to the quasiparticle picture of entanglement propagation in a quantum system. It’s remarkable to see an exactly solvable scenario for a quantity like this, and indeed this work relates to something we were pursuing from a numerical angle, so it’s fantastic to see such a detailed look at something that we had been wracking our brains to try to understand! Although the physical scope of this work is limited, due to the intention of developing an exactly solvable model, there are clear ways that this could be developed in future and applied to other models, and I look forward to seeing these future advances giving us more insights about the behaviour of the negativity and other sophisticated entanglement measures.

**May 6th**

*Tuning between continuous time crystals and many-body scars in long-range XYZ spin chains, by Kieran Bull, Andrew Hallam, Zlatko Papić, and Ivar Martin*: This is a timely one! Following an earlier paper this week, I’ve been thinking a lot recently about time crystals, scars and other systems that exhibit periodic behaviour in time, and one question I’ve been wondering’ is “What’s the fundamental difference between time crystals and scars?”. Well, I need wonder no more, as this paper addresses precisely that question using a long-range XYZ model, and to cut to the chase, concludes that while there are parameter regimes where both types of behaviour can co-exist, they are indeed of fundamentally different origins. The authors even propose experimental measures to distinguish between the two types of behaviour, based around how the system responds following quenches from different initial states. It’s worth noting that the type of time crystal considered here is not the conventionally-studied discrete time crystal, but the less well-known (I think?) continuous time crystal, so keep this in mind when making comparisons with other time crystal papers!