View from the arXiv: Mar 28 - Apr 1 2022
A summary of new preprints appearing on arXiv during the week of Mar 28th to Apr 1st 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)
Dynamic structure factor of the antiferromagnetic Kitaev model in large magnetic fields, by A. Schellenberger, M. Hörmann, and K.P. Schmidt: One of the key concepts in condensed matter physics is the link between the small (e.g. individual electrons) and the large (e.g. a real material that you can hold in your hand). Connecting these two vastly different scales is a huge challenge, and one key technique used to investigate this connection is known as spectroscopy. Loosely speaking, this usually works by firing some photons or neutrons at a sample and watching to see what is absorbed (then re-emitted). From this, experimenters can reconstruct a mathematical quantity known as the dynamic structure factor (DSF) which connects the behaviour of the large system to the quantum mechanical properties of the individual electrons, based on what energies they are able to absorb. Calculating the DSF isn’t easy – and measuring it even less so! – and this paper tackles the challenge of computing the DSF on a particularly complex ‘honeycomb’ lattice. This enables a detailed understanding of the properties of the model in terms of excitations known as quasiparticles, connecting the microscopic behaviour to the observed/calculated macroscopic behaviour. The paper caught my eye because Kai Schmidt, one of the authors, often works with very interesting continous unitary transform techniques, and this is no exception as the technique is used here. This is a nice combination of an unusual theoretical method combined with a challenging system which results in some neat findings!
Random matrix analysis of deep neural network weight matrices, by Matthias Thamm, Max Staats, and Bernd Rosenow: This is a curious paper, and I don’t entirely know what to make of it. It concerns so-called deep neutral networks, and looks at how a ’trained’ network differs from a randomly initialised network. The rough idea is that a neural network stores a huge number of parameters known as ‘weights’, which essentially store the information that allows a neural network to learn from data and enables them to perform amazingly well at a wide range of tasks. This paper studies the weights, and in particular looks at how information is stored in these weights. The surprising finding, at least to me, is that a large fraction of the weights seem to be essentially random, even after the network has been trained. To analyse this, the authors look at the distribution of so-called singular values and show that they match well with the Wigner surmise, a prediction from random matrix theory that describes – as you might expect – randomly distributed matrix elements. The paper doesn’t dwell on the significance of this result, which is something I’d love to know more about. From an outside point of view this suggests that the number of parameters in a trained model could be dramatically reduced without sacrificing performance, and I’d be curious to know if that is indeed the take away from this paper.
Effects of critical correlations on quantum percolation in two dimensions, by Giuseppe De Tomasi, Oliver Hart, Cecilie Glittum, and Claudio Castelnovo: Percolation transitions are an interesting type of phase transition, and their nature in quantum systems is not fully understood. The classical case can be visualised in the following way. Imagine a chessboard, but with all squares made white. Now imagine randomly making some of the white squares black, and introducing a piece that can only move on black squares1. The question is, can this chess piece move freely across the board, or will it be stuck in some particular area? If there are not many black squares, the chess piece will be localised and unable to move very far. As we increase the density of black squares, the piece will find it easier and easier to move until eventually it can go almost everywhere – it’s delocalised. Between these two extremes lies a critical density of black squares which marks the transition between localised and delocalised behaviour. The quantum case is a little harder, as it’s possible for the random distribution of black squares to induce Anderson localisation and prevent the piece from being able to move freely even though it looks like it should be able to. This work studies a complicated variation on this problem, namely a situation in which the black squares are not distributed randomly but instead in a correlated way, finding evidence for an unusual type of emergent disorder related to thermal fluctuations, capable of realising a potentially new class of disorder-free localised systems. All-in-all, a very interesting piece of work sure to stimulate interest in the research community!
Stability of many-body localization in Kicked Ising model, by Piotr Sierant, Maciej Lewenstein, Antonello Scardicchio, and Jakub Zakrzewski: Many-body localization (MBL), which I’ve written about here several times, is a phenomenon where an interacting quantum system can fail to thermalize due to the addition of some sort of disorder. The stability of MBL has recently come into question, as numerically exact methods are restricted to small system sizes and other theoretical approaches are usually more suitable in localised/delocalised phases are rarely able to tackle both at once. This work sets out to find a different class of system which exhibits MBL in a cleaner way that is more amenable to numerical study, and as such examines a periodically driven system known as the ‘Kicked Ising Model’. One main finding is that signatures of MBL are weak in models which exhibit a high degree of symmetry, such as the commonly studied XXZ spin chain, and as such studying models without such symmetries could prove a more fruitful direction for future study to really nail down the nature of the MBL phase, and prove whether it really is stable.
A two-dimensional programmable tweezer array of fermions, by Zoe. Z. Yan, Benjamin M. Spar, Max L. Prichard, Sungjae Chi, Hao-Tian Wei, Eduardo Ibarra-García-Padilla, Kaden R. A. Hazzard, and Waseem S. Bakr: Ultracold atomic gases have become a hugely capable platform for engineering quantum matter on a microscopic scale, enabling precise control over individual atoms. One particular highlight has been the development of optical lattices, which use patterns of laser light to mimic the crystalline structure of a regular solid material and trap the atoms in a periodic lattice made of light. The type of lattice generated depends on the precise setup of the lasers used, and in general the difficulty of readjusting this setup on the fly means that square lattices are the most commonly studied, although there are some exceptions. This work takes the concept a step further by introducing a fully programmable lattice in two-dimensions, which uses the idea of tweezer arrays to hold individual atoms in place at any desired position, allowing essentially arbitrary lattice geometries to be realised in experiments. This could allow for a wide variety of interesting new effects to be investigated in ultracold atomic gases. One question I still have is how this compares to approaches based around spatial light modulators to generate arbitrary patterns, and as I’m not an expert in either approach I’d be very curious to know the answer to this question. [Update: you can check out Kaden Hazzard’s response to this question here!]
Information spreading and scrambling in disorder-free multiple-spin interacting models, by Yoshihito Kuno, Takahiro Orito, and Ikuo Ichinose: The question of how a quantum system relaxes to thermal equilibrium has receieved a lot of attention in recent years, and has rapidly been connected with the question of information spreading and scrambling. In other words, for a system prepared in some form of ordered state, how long does it take for this order to ‘melt’ and become spread out through a system (just as an ice cube in a drink melts on a warm day)? Central to this field of study has been the development of novel entanglement measures which go beyond the relatively well-known bipartite entanglement entropy measures and are capable of a more fine-grained examination of how various parts of a system are entangled with other parts. This paper takes a look at a quantity called the tripartite mutual information, and examines what this tells us about information spreading in a system with unusual three- and four-body interaction terms.
Critical metallic phase in the overdoped random t-J model, by Maine Christos, Darshan G. Joshi, Subir Sachdev, and Maria Tikhanovskaya: Understanding the nature of copper-oxide (cuprate) based superconductors has been a major challenge in solid state physics for quite some time now, and theoretical efforts in this direction have led to the development of a class of models known as Sachdev-Ye-Kitaev (SYK) models which turn out to have many remarkable properties, and even deep links with exotic gravitational phenomena such as black holes. This paper studies an SYK-like model that is related to the t-J model (so famous that it has a Wikipedia page…!) in an effort to understand the unusual metallic phase found in cuprate superconductors. My main interest in this paper is that the authors find a spin glass phase at low temperatures, something which is absent in the typical SYK model. The t-J model is also quite interesting from the point of view of many-body localisation, and so seeing a spin glass ground state established here in this work is very interesting indeed for future efforts to understand the interplay of glassiness and quantum localised phases, not to mention the relevance to the long-standing problem of understanding the ‘strange metal’ phase of the cuprates.
Let’s say it’s a queen, because I don’t want to get into the statistics of what the percolation transition would look like for a rook or a bishop…although that could be an interesting curiosity for a future blog post! ↩︎