# View from the arXiv: Apr 25 - Apr 29 2022

A summary of new preprints appearing on arXiv during the week of Apr 25th to Apr 29th 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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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**Apr 25th**

*Metastates and Replica Symmetry Breaking, by C.M. Newman, N. Read, and D.L. Stein*: This mini-review – which seems to be part of some longer collection of works on the topic of replica symmetry breaking – deals with the concept of *metastates* in disordered systems such as spin glasses. To give some context to the problem, one of the difficulties in studying glassy systems is that at low temperatures they exhibit a large number of (near)-degenerate states which may be largely unrelated to each other, e.g. cannot be transformed into one another by some global symmetry like a spin rotation. This can present a problem for many theoretical methods. This paper phrases the problem in terms of *metastates*, and shows how they provide a tool to understand the complex behaviour of glasses. In much of statistical mechanics, it’s possible to start from a system of finite volume and extrapolate to the thermodynamic limit (infinite system size limit) to abstract away any microscopic details and reach a description of the system only in terms of global properties. Usually this is a well-defined mathematical operation, but in spin glasses this isn’t the case. Indeed, because there are so many possible degenerate states, the procedure of taking the thermodynamic limit can be quite sensitive to the initial configuration that’s being considered, in contrast to more conventional condensed matter systems. Developing theoretical tools capable of navigating this infinitely complex landscape of near-degenerate states is a major challenge, and this work reviews one particular approach to doing this which sheds some light on the inner nature of spin glasses.

*Observation of 1/k^4-tails in the asymptotic momentum distribution of Bose polarons, by Hugo Cayla, Pietro Massignan, Thierry Giamarchi, Alain Aspect, Christoph I. Westbrook, and David Clément*: This work addresses some puzzling experimental observations from a few years ago in which the momentum distribution of an expanding Bose-Einstein condensate was measured and shown to have a peculiar algebraic tail that decayed like *1/k^4* (where *k* is the momentum). This work shows that the peculiar tail seen in the momentum distribution is related to the presence of impurities in the system, and confirms this by showing that the strength of the algebraic tail varies with impurity density, vanishing entirely when the impurities are not present. Interestingly, however, there is still no first-principles understanding of precisely how the impurities cause this effect, and the paper ends with a call to arms for further detail studies of the exact expansion dynamics of the condensate in order to better understand the origin of the observed effect. This work is mostly of fundamental interest to how impurities can affect the propagation of quantum gases, but if that’s the sort of thing you’re interested in (and I am…!) then it’s an interesting read.

**Apr 26th**

*Many-body localization of one-dimensional degenerate Fermi gases with cavity-assisted non-local quasiperiodic interactions, by Jianwen Jie, Qingze Guan, and Jian-Song Pan*: Many-body localisation (MBL) is by now on reasonably firm ground in one-dimensional systems with short-range interactions, but in higher-dimensional systems the fate of MBL is less well established. This is also true for one-dimensional systems with long-range interactions (which in some senses behave like higher-dimensional systems anyway). As the study of long-range interactions is generally computationally challenging, relatively few works exist which have looked at this scenario, particularly in very large systems. This work motivates the study of long-range interactions by putting the system of interest in a cavity, which generates a long-range quasi-periodic interaction of an interesting type that I haven’t seen before. In particular, the disorder is *only* in the interaction term, and there is no on-site term as in typical models of MBL. The authors use exact diagonalisation to investigate various aspects of the model, and conclude that localisation behaviour survives the presence of long-range interactions, and suggest that this could lead to interesting applications for the non-destructive investigation of MBL by measuring photons emitted from the cavity rather than the localised system itself. This is an intriguing suggestion, and something I’d love to work on myself!

**Apr 27th**

*A New Era of Quantum Materials Mastery and Quantum Simulators In and Out of Equilibrium, by Dante M. Kennes, and Angel Rubio*: Recent advances in the controllability of quantum matter have led to some fascinating developments, not just in systems like ultracold atomic gases which are commonly talked about as paradigms of highly controllable quantum matter, but also in solid state systems where the properties of materials can be controlled by the application of light. (Or, by shooting stuff with lasers, if you want to phrase it in a more exciting sci-fi kind of way!) This review – to be published in Sketches of Physics: The Celebration Collection – looks not just as ways in which the properties of quantum materials can be tuned using laser light, but also surveys how exotic *non-equilibrium* physics can be realised in these systems, which is a fascinating frontier full of untapped potential.

*A comprehensive review on topological superconducting materials and interfaces, by M. M. Sharma, Prince Sharma, N.K. Karn, and V.P.S. Awana*: The second of two reviews today, this much much longer, more niche and far more technical, but every bit as interesting as the previous one. This work looks at superconductivity in topological materials and the link with the still-elusive Majorana quasiparticles which are the subject of much controversy and it is not yet clear whether they have been definitively observed. The focus of this work, however, is on real materials which are candidate topological superconductors, with a thorough exploration of the properties the materials must satisfy in order to be declared as topological superconductors. For a theorist like me, a lot of the details here go a little over my head but this looks like a good resource for anyone wanting to know what the current state of the art is in the field of topological superconductors.

**Apr 28th**

*Correlated metallic two-particle bound states in Wannier–Stark flatbands, by Arindam Mallick, Alexei Andreanov, and Sergej Flach*: Wannier-Stark localisation is a surprising phenomenon that occurs when a non-interacting quantum system is subject to a uniform external field (i.e. a linear on-site potential). Despite being entirely translationally invariant, the eigenstates of this system are in fact localised. Even more surprisingly, the localisation is Bessel-function-like, and decays even faster than the exponential localisation in a disordered system such as an Anderson insulator. This work studies what happens to a pair of Wannier-Stark localised particles when an on-site contact interaction is added, and finds that the localisation is partially destroyed and that propagating metallic states emerge. This has some interesting applications towards studies of many-body localisation in disorder-free systems, although to date the major works in this domain use spinless fermions, so may have to be modified to study this form of interaction. I’ll be very curious to see if this work is extended in the future to one-dimensional systems which have been studied in the context of many-body localisation, as Wannier-Stark localisation has many strange properties that would be extremely interesting to understand better using the sorts of tools developed in this work.

**Apr 29th**

*Persistent homology analysis of a generalized Aubry-André-Harper model, by Yu He, Shiqi Xia, Dimitris G. Angelakis, Daohong Song, Zhigang Chen, and Daniel Leykam*: The Aubry-André-Harper (AAH) model describes non-interacting quantum particles (which can be fermions or bosons, and I don’t think this paper specifies which case they consider) moving in a quasiperiodic potential. This is an interesting intermediate case that exists between a clean, translationally invariant delocalised system and a fully random, Anderson localised model. As a result, even the non-interacting model in one dimension has a phase transition between localised and delocalised states. The authors of this paper study the phase diagram of the AAH model using the technique of persistent homology, which is new to me. The idea, as they describe it, is to calculate topological features across a range of different length scales and record at which length scales interesting features appear or disappear. They argue that this measure is sensitive to features and subtle structure that other methods can miss, and they present some interesting results to back up this claim. This is definitely a technique I’d like to investigate in more detail.

*Dynamical purification and the emergence of quantum state designs from the projected ensemble, by Matteo Ippoliti, and Wen Wei Ho*: I’ll start this summary by saying that I really don’t understand most of this paper, but that I’d really like to! This work studies how quantum systems thermalise in an interesting way that’s quite new to me, based on quantum state designs, a concept from quantum information theory. The motivation is that the authors want to study an intriguing emergent universal behaviour of a set of states known as the projected ensemble, a way of understanding thermalisation from a different point of view that the more standard density matrix picture. A key part of the method is the idea of dual-unitarity, the property of (1+1)-dimensional quantum circuits which are unitary in both time and space, enabling some interesting mathematical tools to be used. This work connects to concepts including information scrambling and quantum chaos (in the sense of ergodic systems which thermalise under their own dynamics), and insofar as I understand this work at all, it looks like a very interesting and novel perspective on these still-enigmatic phenomena.

*Protecting coherence from environment via Stark many-body localization in a Quantum-Dot Simulator, by Subhajit Sarkar, and Berislav Buca*: In one of this week’s other papers, we looked at the phenomenon of Wannier-Stark localisation in non-interacting systems. This work studies the *interacting* analog, known as Stark MBL^{1}, and investigates the questions of how stable this form of localisation is to external thermal baths – in this case made up of phonons – and whether the resulting local integrals of motion (*l*-bits) are sufficiently stable to be candidates for quantum computation. The authors present evidence that these *l*-bits are indeed protected from external noise for exponentially long times, potentially enabling them to be used as candidates for quantum computation, not just as a quantum memory (as often motivated in works studying localisation) but also for gate operations in semiconductor devices, which could be an interesting and novel platform for future quantum technologies.