View from the arXiv: Jun 6 - Jun 10 2022
A summary of new preprints appearing on arXiv during the week of June 6th to June 10th 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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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A simple model for strange metallic behavior, by Sutapa Samanta, Hareram Swain, Benoît Douçot, Giuseppe Policastro, and Ayan Mukhopadhyay: A major outstanding problem in modern condensed matter physics that I don’t often feature in these pages, so-called strange metals are metallic phases with unusual electronic properties that first arose in the context of studies of superconductivity. The idea is that the strange metal phase is formed by an underlying quantum critical point in doped materials, but many of its features remain hard to understand and there is still a need for simple effective models that may shed some light on the complex behaviour observed in more realistic models which exhibit strange metal behaviour. This paper analyses a (relatively…!) simple model proposed previously and demonstrates that it fits real experimental data very well, suggesting that it provides a good description of the strange metal phase. I particularly love one of the concluding sentences of the paper, which is a great example of what I consider to be a non-standard use of the word ‘simple’: “For our simple model to be more realistic…we should consider a lattice of AdS2 black holes…”.
Eigenvalue ratio statistics of complex networks: Disorder vs. Randomness, by Ankit Mishra, Tanu Raghav, and Sarika Jalan: This one caught my eye because of the title, as ‘disorder’ and ‘randomness’ are two words I often use interchangeably. Here, it means ‘random’ in the sense of ‘random matrix theory’, a framework that has found many applications in the study of localised systems but which takes its name from the study of random matrices in the context of ergodic/chaotic systems, which are the opposite of localised. Random matrices turn out to exhibit some of the same mathematical properties as quantum chaotic systems, and so the study of these matrices is one way to understand chaotic quantum matter. It also provides a useful tool for understanding when a quantum system is no longer chaotic, as its mathematical properties will stop agreeing with random matrix theory. This work is a detailed look at a quantity known as energy level spacing statistics, which are used a lot in disordered systems to distinguish localised/integrable systems from ergodic/chaotic ones. I have the impression that this became a quantity of interest in quantum systems through a combination of necessity and a fantastic insight from Vadim Oganesyan and David Huse that turned it into a practical tool that is by now widely used, however there are few rigorous mathematical investigations of this quantity outside of the cond-mat/atomic-phys community, so this paper is nice to see.
Avoiding barren plateaus via transferability of smooth solutions in Hamiltonian Variational Ansatz, by Antonio Anna Mele, Glen Bigan Mbeng, Giuseppe Ernesto Santoro, Mario Collura, and Pietro Torta: The frantic search for practical applications of current and near-term quantum computing hardware is a hugely active and exciting field of research, but with a lot of challenges still to be solved. One particular application is the field of Variational Quantum Algorithms (VQAs), which is a way of using quantum hardware (combined with a classical optimisation step) to variationally find the ground state of a given Hamiltonian. One problem with this approach is that the optimisation step can run into situations where the quality of the solution doesn’t change much as the parameters are varied, a situation referred to as a ‘barren plateau’, and therefore the optimisation slows down as the best solution becomes very hard to find. Finding ways to avoid or eliminate these barren plateaus is a key step in making VQAs practical. This work proposes a way of avoiding such problems by first solving small systems, where such problems are not as severe, and then using the solution from the small system as a initial guess for the application of the method to larger systems. This is a neat way to avoid the issue and seems to work really well. I’m particularly intrigued by one of the concluding sentences that mentions application of this in two dimensions, potentially with disorder…!
Probing finite-temperature observables in quantum simulators with short-time dynamics, by Alexander Schuckert, Annabelle Bohrdt, Eleanor Crane, and Michael Knap: Quantum simulators – such as ultracold atomic gases or trapped ions – feature often in these pages as they’re incredible feats of experimental engineering that enable direct investigation of many complex properties of quantum systems that can be either challenging for theoretical methods, or sometimes entirely out of reach. One problem with them is that, ironically, the isolation of quantum simulators from their environments is now so good that it’s hard to prepare finite-temperature states, as you’re essentially stuck with whatever the energy density of your initial non-equilibrium state is (e.g. the commonly-studied charge density wave, often used as a way to probe the ‘infinite temperature’ properties of a model). This work proposes a way to investigate finite temperature properties – and even low temperature properties – of quantum systems using quantum simulators. The key step is the Jarzynski equality, which links equilibrium properties to non-equilibrium properties, and can itself be constructed from measurements of a property known as the Loschmidt echo. The authors show that their method is robust to realistic sources of noise, and provide benchmarks demonstrating that it is capable of detecting the finite-temperature phase transition in the transverse-field Ising model with long-range interactions. It will be interesting to see how the use of this algorithm develops in the near future, and whether it will allow quantum simulators to shed light on some major unsolved problems in quantum condensed matter relating to the low-temperature properties of models which are extremely challenging to solve using most other methods.
Robust quantum boomerang effect in non-Hermitian systems, by Flavio Noronha, José A. S. Lourenço, and Tommaso Macrì: The quantum boomerang effect is a really interesting feature of disordered systems whereby a wavepacket with non-zero velocity can scatter from a random potential and return to its original position, then stop there. This is in contrast with the more commonly studied example of Anderson localisation, where normally we think of localised wavefunctions as the equilibrium eigenstates of the problem, but rarely consider dynamical phenomena of this type. This work extends previous studies of the quantum boomerang effect to non-Hermitian Hamiltonians, and makes a thorough analysis of the role of different symmetries on the stability of the boomerang effect. The outlook of this paper is particularly interesting, suggesting that the presence or absence of the boomerang effect can be used as a probe of the properties of a given quantum system, and raising the question of whether or not the boomerang effect survives the presence of interactions and many-body localisation. (Naively I’d guess it probably does for strong enough disorder, but it would be very interesting to see if this is indeed the case!)
Quantum information spreading in random spin chains, by Paola Ruggiero, and Xhek Turkeshi: Understanding how quantum information and entanglement propagate in many-body quantum systems is a major challenge in modern many-body physics. There are many approaches to this, such as numerical methods or various analytical approximations, but this is an interesting work that builds on a dynamical real-space renormalisation group procedure developed for spin chains with strong random disorder, and extracts some intriguing results about multipartite entanglement in many-body quantum systems. It’s mainly analytical in nature, with some numerical results for non-interacting systems at the end, and it’s quite a remarkable how much insight the authors have been able to develop for such a complex problem. In the future I’d love to see further numerics on interacting systems to see just how closely the exact or quasi-exact numerical results would agree with the analytical predictions in this paper, but that’s beyond the scope of this particular work. (Personally I find this work really interesting as Marco Schiró and I looked into a similar RG method several years ago before developing our flow equation approach, and more recently I’ve been involved in studies of information propagation and entanglement negativity, so it feels like all my interests perfectly align in this paper…!)
Some rare days, nothing on the arXiv catches my eye, and this was one of those days…!
Computational advantage of quantum random sampling, by Dominik Hangleiter, and Jens Eisert: Despite being in a group led by one of the co-authors of this work, in which a lot of people work on ‘random sampling’, I have until now had very little idea what it is, or why it’s a leading candidate for quantum systems to demonstrate a convincing advantage over classical systems. This monster 81 page review covers everything I ever wanted to know about random sampling, and more! This paper covers the theoretical underpinnings and motivation for random sampling, some more practical/experimental considerations and a look at open problems. This is one that I fully intend to read in more detail, as I’d love to understand better what most of my colleagues here work on…!