View from the arXiv: Apr 4 - Apr 8 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)

Apr 4th

Quantum approximate optimization algorithm for qudit systems with long-range interactions, by Yannick Deller, Sebastian Schmitt, Maciej Lewenstein, Steve Lenk, Marika Federer, Fred Jendrzejewski, Philipp Hauke, Valentin Kasper: In most descriptions of quantum computers, people usually assume that the basic building blocks are objects known as qubits (‘quantum bits’) which have two quantum states (usually labelled |0> and |1>), which differ from classical bits in that they are allowed to be in a superposition of both states rather than just one or the other. It’s also possible, however, to build quantum computers from objects with more than two available states, so-called ‘qudits’, and that’s what this paper considers. The authors look at an algorithm known as the Quantum Approximate Optimixation Algorithm (QAOA). This is a method that can be used on quantum computers to prepare a desired quantum state, for example the ground state of a given Hamiltonian, and as such it’s a useful algorithm to be able to implement efficiently. In this paper, the authors consider what this algorithm would look like for qudits rather than qubits, and showed how it can be applied to a variety of optimisation problems, demonstrating that it is a promising technique for further development.

Chaos enhancement in large-spin chains, by Yael Lebel, Lea F. Santos, and Yevgeny Bar Lev: Understanding chaos remains a major challenge in physics, not least because there are several slightly different definitions and it may mean different things to different people. In this paper, the authors study quantum chaos, which means that the energy levels of a quantum system exhibit the same properties as the eigenvalues of random matrices. This is something often studied in the context of localisation and thermalisation, and indeed ‘chaos’ in this sense is commonly taken as symonymous with ’thermalisation’. The authors of this paper take a model that has been extensively studied in the many-body localisation community, and instead of looking at localisation, they instead look at the opposite limit of weak disorder and examine the signatures of chaotic behaviour. In particular, they examine the effects of ’large’ spins (i.e. not spin-1/2), and demonstrate that despite the classical model exhibiting chaos, the quantum model seems significantly less chaotic. Fear not, however, because the authors investigate the origin of this effect and propose two ways by which chaos can be enhanced, which they demonstrate seem to work well for the quantum model despite having little effect on the classical system. This is a really interesting work that suggests quantum and classical chaos may not always go hand-in-hand, something which I’d guess could also be understood in terms of weak localization effects.

Apr 5th

Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase, by Giuseppe De Tomasi, and Ivan M. Khaymovich: Amongst the frantic study of localisation and chaos, a relatively new area of research has sprung up that lies directly between these two limiting cases. There are systems which don’t thermalise, but also don’t appear to be fully localised. These are important because understanding them could help shed light on the stability of localised phases. This manuscript studies one such case, known as ’non-ergodic-extended’ (NEE) states, and it looks at them in a non-Hermitian random matrix model. Normally in condensed matter we always think about Hermitian systems, which means that all of their energy eigenvalues are real and their energy is conserved. Non-Hermitian systems are interesting because they describe physical systems which are coupled to an environment, able to gain and/or lose energy, and as such they exhibit very different behaviour to their equilibrium counterparts. The authors of this work want to study what happens to these ‘intermediate’ NEE states in a non-Hermitian system, and contrast this with localisation effects which are known to be stable in non-Hermitian models. Interestingly, it seems that this intermediate phases can persist in such models if the on-site potential is purely real or purely imaginary, but for a complex potential (i.e. with both real and imaginary parts), this intermediate phase is destroyed and instead replaced by a fully localised phase. This is a very interesting observation, and I’d be very curious to understand this further.

Apr 6th

Strongly-interacting bosons at 2D-1D Dimensional Crossover, by Hepeng Yao, Lorenzo Pizzino, and Thierry Giamarchi: In theoretical physics, we often study systems in one dimension, two dimensions, or three dimensions¹, and it’s by now well-established that the dimensionality can have a big effect on the physical behaviour of a given system. In one dimension, quantum effects are felt more strongly and this leads to certain phases that can’t exist in two dimensions, such as the Tomonaga-Luttinger liquid. Normally, the dimensionality of a system is fixed, but what if we could vary it? That might sound like science fiction, but it’s the question asked by the authors of this study, who consider what happens to an ultracold gas of bosons arranged in coupled one-dimensional tubes. When the coupling is zero, the one-dimensional tubes are completely cut off from one another and exhibit typical one-dimensional effects. When the coupling is strong, on the other hand, the tubes connect togther and form a two-dimensional system. By varying the strength of this coupling, the authors can effectively tune their system continuously from one to two dimensions and study what happens during this process. This is a fascinating work that makes fantastic use of quantum Monte Carlo methods to study the different phases of the model as it is varied from one to two dimensions, and provides clear predictions that can be checked in current-generation experiments.

Apr 7th

A Variational Ansatz for the Ground State of the Quantum Sherrington-Kirkpatrick Model, by Paul M. Schindler, Tommaso Guaita, Tao Shi, Eugene Demler, J. Ignacio Cirac: The Sherrington-Kirkpatrick model is a famous (…to a certain type of physicist, at least) model that describes a spin glass phase, an enigmatic phase of matter characterised by a failure of a system to reach thermal equilibrium at low temperatures and extremely slow non-equilibrium dynamics. Glasses are often studied in classical systems and/or using mean-field methods, and comparatively little is known about their quantum mechanical properties (although it’s something I, and many others, are working on!). In particular, one thing that’s very hard to study is the entanglement properties of a quantum glass, as many conventional methods give access to observables rather than states. This work develops an approximate method for the computation of the ground state of the quantum Sherrington-Kirkpatrick model, opening a door for the further study of spin glass ground states in strongly quantum mechanical models and the development of a detailed understanding of their entanglement properties. A curious feature of this ansatz is that all signs of a phase transition vanish whenever a longitudinal field is applied, and I’d be interested to know if this is due to some limitation of the ansatz, or a sign of unusual interesting physics. Only time will tell…!

Apr 8th

Generalized Symmetries in Condensed Matter, by John McGreevy: The concept of symmetry underpins a lot of condensed matter physics. One of the main ways in which we classify phases of matter is by the symmetries they exhibit, and the symmetries that they break. The thing is, this picture turns out to be a little too straightforward, and doesn’t capture some particularly interesting phases of matter. This review article argues for a ‘Generalized Landau Paradigm’ which goes beyond the standard Landau symmetry-breaking picture, and though it doesn’t touch upon disorder or non-equilibrium dynamics (my usual favourite subjects), the viewpoint put forward in this article is definitely an interesting one!

Effective field theory of random quantum circuits, by Yunxiang Liao, and Victor Galitski: This one caught my eye because I’m familiar with field theory, but only begun to learn about quantum circuits recently. The idea here is to break away from the ‘bottom up’ approach to studying quantum circuits, where a detailed simulation is conducted that keeps track of all microscopic details, and instead move towards a ‘big picture’ approach where unimportant details are neglected and only the so-called ‘universal’ features are kept track of. This approach can allow for deeper and more fundamental insights at the cost of losing track of specific details of the model under consideration, however as long as there is reason to believe these details are not important then this sort of framework can be very powerful. The main aim here is to develop a field theory approach for random quantum circuits. The authors then use this method to derive the random matrix theory (RMT) spectral statistics already seen in some specific models, and also extend this finding to show that RMT spectral statistics are perhaps more robust and more widespread in random quantum circuits than has been previously shown. This work appeals to me, as it’s really nice to see powerful field theoretical methods applied to this sort of problem.