# View from the arXiv: Feb 21 - Feb 25 2022

A summary of new preprints appearing on arXiv during the week of Feb 21st to Feb 25th 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)

**Feb 21st**

*A stabilization mechanism for many-body localization in two dimensions, by D. C. W. Foo, N. Swain, P. Sengupta, G. Lemarié, and S. Adam*: Could this be one of the biggest developments in many-body localisation (MBL) for some time? It’s possible! The question of whether MBL is stable in two dimensions has remained unsettled for some time. While numerical results, including some of mine, have suggested the stability of MBL in two dimensions, others have made reasonable arguments that suggest this phase is ultimately unstable. In this work, the authors study the effect of a confining potential of a sort always present in experiments, but rarely considered in theoretical calculations. They find that in non-interacting systems, the confining potential results in LIOMs which decay faster-than-exponentally, allowing them to bypass the established avalanche mechanism that would result in delocalisation for typical exponentially decaying LIOMs. On the one hand, this makes a lot of sense and isn’t so surprising - faster than exponential decay means that the LIOMs interact so weakly they’re almost non-interacting - but on the other hand, this is still a very novel result. It would be very interesting to see what methods designed to explicitly construct LIOMs can do in two dimensions, and whether the effect of a confining potential can stabilise MBL in one-dimensional systems with long-range interactions.

*Scalable approach to many-body localization via quantum data, by Alexander Gresch, Lennart Bittel, and Martin Kliesch*: Continuing today’s theme of many-body localisation, and along the lines of something I’ve been thinking about myself, this work investigates whether it’s possible to use machine learning to take a particular random disorder realisation as an input and return useful information about the localisation properties of the system as an output. The authors show that their method can produce reasonable looking outputs for system sizes larger than the training dataset used (although I guess that the further the system size from the training dataset, the lower the accuracy will become?) and that it may be a useful computational tool in getting more from the data obtained using other methods, allowing a neural network to ’learn’ key features of the system and then skip the most computationally intensive steps of the simulation, jumping directly to the useful output data. I’d be very interested to see this used to compute LIOMs…watch this space!

**Feb 22nd**

*Reentrant localization transition in the Su-Schrieffer-Heeger model with random-dimer disorder, by Zheng-Wei Zuo, and Dawei Kang*: The interplay between disorder and topology is fascinating, and as yet not very widely studied. Topological systems themselves are both of fundamental interest, and possibly of future technological use, but as disorder is present in almost any real material in the form of random impurities, it’s crucial to understand how these impurities may affect the sought-after topological properties. This work studies a one-dimensional model with interesting topological features known as the Su-Schrieffer-Heeger (SSH) model, which somewhat to my surprise is a non-interacting system - I sometimes forget that many-body interactions aren’t necessarily required for the physics of a system to be interesting! The authors map out the phase diagram of the SSH model in the presence of disorder and show that randomness favours a metallic phase, but that a topologically non-trivial phase can survive. The find a ‘reentrant’ transition in the topologically trivial phase, i.e. a situation where the system is insulating at zero disorder, becomes metallic at moderate disorder, but then becomes interesting again at strong disorder. This is unusual, but very interesting, and makes me wonder what other secrets this seemingly innocuous model may hold when disorder is added!

**Feb 23rd**

*Many-body localization and delocalization dynamics in the thermodynamic limit, by Jonas Richter, and Arijeet Pal*: The development of good numerical methods for simulations of many-body localised phases of matter remains an outstanding challenge in the field, and one of critical importance in the quest to fully characterise the stability of many-body localisation. This work outlines the use of a numerical linked cluster expansion (NLCE) method, a relatively new technique for the study of disordered systems which (when sufficiently converged) is able to bypass the finite-size effects inherent in other methods. The authors study the spin-1/2 two leg ladder and the Fermi-Hubbard model, both of which are challenging for other methods, and establish the usefulness of the method, ending with an outlook towards further outstanding challenges such as the nature of localization in two dimensions.

*Cold atoms in low dimensions – a laboratory for quantum dynamics, by S.I. Mistakidis, A.G. Volosniev, R.E. Barfknecht, T. Fogarty, Th. Busch, A. Foerster, P. Schmelcher, and N.T. Zinner*: Ultracold atomic gases are one of the most well established platforms for quantum simulation, and over the years and decades there has been a vast amount of work studying and understanding them. This comprehensive review serves as a guide to the field, taking in a wide range of different models and theoretical methods applicable to ultracold atoms, as well as an overview of cutting edge developments and interesting future directions that will occupy researchers in the years to come.

**Feb 24th**

*Going beyond ER=EPR in the SYK model, by Micha Berkooz, Nadav Brukner, Simon F. Ross, and Masataka Watanabe*: I’ve been getting more and more interested in SYK models again recently, in part due to an upcoming work on the topic (out soon - watch this space!) and in part due to its status as an interesting playground at the intersection of disordered systems, complexity and even gravitational studies. Although lengthy and written in more of a high-energy than condensed matter language, this paper considers some interesting connections between entanglement and wormholes, and in particular the authors study a particular construction known as a thermofield double state which allows the link between the geometry of the dual gravitational theory (i.e. a wormhole description) and entanglement to be probed. The authors argue that entanglement alone is not enough to facilitate a wormhole description, and investigate in detail just what ingredients are required.

*Strong photon interactions from weakly interacting particles, by Arturo Camacho-Guardian, Miguel Bastarrachea-Magnani, Thomas Pohl, and Georg M. Bruun*: Photons - quanta of light - are unlike typical quantum particles in many ways, but perhaps one of the less obvious ways is that they do not interact with each other. Photons only interact with matter (with charged matter, in fact) and not with each other, however recent advances in light-matter couplings have enabled the engineering of an effective interaction between photons. Loosely, one photon interacts with a piece of matter, then this matter interacts with another photon, and this mimics the effect of the two photons directly interacting with each other. Until now, this ‘fake’ interaction between photons has been very weak, however this new work proposes a way to realise much stronger interactions between photons. While there are technological applications for this, my interest lies more in the fundamental aspects - engineering photon-photon interactions could allow for the realisation of all manner of new physics unlike other more conventional condensed matter platforms.

**Feb 25th**

*Dissipative time crystal in an atom-cavity system: Influence of trap and competing interactions, by Richelle Jade L. Tuquero, Jim Skulte, Ludwig Mathey, and Jayson G. Cosme*: Time crystals are a fascinating phase of matter that get a lot of attention because of their name, but behind the sci-fi sounding title hides a lot of novel and unusual physics. I’m familiar with time crystals in the case of periodic drive applied to a disordered system, but this work studies them in a different context. Here, the authors look at a model where *dissipation* is key, with a theoretical setup that considers an atomic condensate inside an optical cavity in a manner that resembles an open Dicke model. The authors consider a model typically solved in the mean-field limit, and ask what happens if they add more realistic experimental constraints in the form of a harmonic trapping potential and short-range interactions. They find that the time crystal behaviour does indeed remain stable to weak perturbations of these forms, and that a metastable time crystal phase can also be found for some choices of interaction strengths. This is an interesting, valuable study away from the ideal mean-field limit and shows the effect of various real experimental/physics constraints on the behaviour of a time crystal, which may help to understand how we can engineer these sorts of exotic non-equilibrium phases in a robust manner.

*Topological Anderson insulators induced by random binary disorders, by Shu-Na Liu, Guo-Qing Zhang, Ling-Zhi Tang, and Dan-Wei Zhang*: Just a quick one, but as we’ve already looked at one paper about disorder in the SSH model this week, I thought I’d briefly highlight another paper on the same topic that appeared today. This work looks at the interplay of topology and disorder, and how the topological Anderson insulator can emerge in various parameter regimes. If you found the previous paper on the SSH model interesting, you may want to check this one out as well!