View from the arXiv: Mar 14 - Mar 18 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)

Mar 14th

Electronic structure of the highly conductive perovskite oxide SrMoO3, by E. Cappelli, A. Hampel, A. Chikina, E. Bonini Guedes, G. Gatti, A. Hunter, J. Issing, N. Biskup, M. Varela, Cyrus E. Dreyer, A. Tamai, A. Georges, F.Y. Bruno, M. Radovic, and F. Baumberger: Something a little different this week, as electronic structure papers don’t usually catch my eye, but this one had several ‘key words’ that jumped out at me¹. The aim of this work is to understand the electronic properties of the material (e.g. the resistivity, which is strangely low when compared to other similar materials) using a method known as ‘angle-resolved photoemission spectroscopy’ (ARPES), which essentially involves shining a laser on a metal and seeing how the photons are reflected from it. As photons interact only with charged particles, and as they’re far more likely to interact with electrons than with protons in atomic nuclei, using this data allows the researchers to reverse-engineer properties of the conducting electrons from the photoemission experiments. This particular material (SrMoO3) sounds like a challenging one to understand, both from the experimental point of view and the theoretical one. The authors conclude that the electrons do not strongly interact with phonons (lattice vibrations) in this material, and that the electron-electron interactions alone are responsible for the surprising thermodynamic properties of the material seen in previous experiments, but leave the theoretical interpretation open for the time being - room for future follow up work, in other words!

CALiPPSO: A Linear Programming Algorithm for Jamming Hard Spheres, by Claudia Artiaco, Rafael Díaz Hernández Rojas, Giorgio Parisi, and Federico Ricci-Tersenghi: Imagine taking an empty box, and filling it with marbles: while there are only a few marbles in the box, they are free to roll around and move, but once enough marbles are added, eventually there are too many of them and they cease being able to move. The point at which the marbles (hard spheres, in the language of this paper) stop moving is known as the jamming transition, and despite how simple it is to sketch the general idea, understanding this transition in full detail is a tough problem. This work introduces a new algorithm known as ‘Chain of Approximate Linear Programming for Packing Spherical Objects’ (CALiPPSO) and an accompanying Julia package to study this jamming transition numerically. The key insight is recasting the hard problem (jamming of hard spheres) as a simpler linear optimisation problem. This paper and the Julia package that goes with it represent an interesting development in the field of numerical simulation of jamming transitions, and I’ll be curious to see what future uses this algorithm is put to.

Mar 15th

Disorder-free localization transition in a two-dimensional lattice gauge theory, by Nilotpal Chakraborty, Markus Heyl, Petr Karpov, and Roderich Moessner: The exploration of exotic systems which break ergodicity continues in this intriguing new work which examines disorder-free localization in an unusual two-dimensional model. Localization – the inability of a particle to move beyond some specific distance – is relatively easy to achieve in strongly disordered matter, but the nature of randomness is that it can be hard to study and hard to characterise. Recently, people have moved away from random disorder and begun to look for similar localization effects in non-random quantum systems. This new work is another step along this road, with the authors considering a model known as the U(1) quantum link model, which is a bit of a mouthful. The idea is that so-called lattice gauge theories are disorder-free models which possess a rich internal structure that leads to a form of self-induced emergent disorder that acts on the non-equilibrium dynamics, leading to typical localization phenomena. This work studies such a model in two dimensions, historically a difficult middle ground between strongly quantum (d=1) and ’easier’, more classical problems (d>2). The authors investigate the localization phase transition and its associated universality class, and conclude that it is the same as the so-called percolation transition in two dimensions. This is interesting, and possibly quite telling, as the percolation transition is far more suggestive of glassy dynamics that quantum localization: lattice gauge theories could be a very fruitful environment for further study of the interplay between quantum localization phenomena (Anderson, or many-body localization) and glassiness, a topic close to my own work.

Schrieffer-Wolff Transformations for Experiments: Dynamically Suppressing Virtual Doublon-Hole Excitations in a Fermi-Hubbard Simulator, by Anant Kale, Jakob Hendrik Huhn, Muqing Xu, Lev Haldar Kendrick, Martin Lebrat, Fabian Grusdt, Annabelle Bohrdt, and Markus Greiner: One important way of getting a handle on the behaviour of impossibly complex quantum systems is to separate out the low-energy dynamics (usually the bit we’re interested in) from the high energy dynamics (usually the bit we don’t care about), and discard the latter from our calculations. This reduces the complexity of the problem, and helps us focus our efforts on the most relevant bits of physics that we want to study. Unitary transforms are one of the mathematical procedures we use that can help to do this, as it allows us to split our problem into separate ’low’ and ‘high’ energy sectors, allowing us to immediately discard the sector we don’t want to investigate. One way of doing this is a Schrieffer-Wolff transform, and it’s a very common theoretical tool. This papers implements the Schrieffer-Wolff transform in an experiment, which is kind of incredible and something I’d never even considered could be possible. The idea is that it’s experimentally possible to approximately make the unitary transform that separates the low- and high-energy sectors of the theory, allowing experimenters to directly study the same low-energy models that theorists use. One feature that I find particularly intriguing is that although the authors called it a Schrieffer-Wolff transform, the transform made in the experiment looks to have a lot in common with the continuous unitary transforms that I work with. I’d be very curious to know if this analogy goes deeper than purely cosmetic!

Inverse Hamiltonian design by automatic differentiation, by Koji Inui, and Yukitoshi Motome: Another unusual one from me, but this paper is here because the title alarmed me, as it sounded a lot like something I’m working on with a colleague! Happily, it turns out to be very different, but this momentary panic gave me reason to read this paper and discover this extremely interesting work. The idea here is to harness a powerful numerical procedure called automatic differentiation to allow the efficient design and optimisation of particular quantum models, through a mathematical object known as the Hamiltonian (which will be very familiar to any quantum physicists reading this!). A Hamiltonian is, in a sense, a complete description of a quantum system that captures almost all of its physical properties. A goal of materials science is to be able to find Hamiltonians that exhibit particularly desirable properties, and this paper proposes a way to do that. First, an initial Hamiltonian is chosen, which likely won’t have the desired properties. Next, using automatic differentation, the Hamiltonian is modified slightly in the hope that this will enhance the desired properties. Said properties are then re-computed for the modified Hamiltonian, and this procedure is repeated until we obtain a final Hamiltonian that exhibits the desired physical properties. While relatively simple in concept, the key ingredient here is the use of automatic differentation to do the heavy lifting. I’m no expert on the particular details of this work, but I find the concept fascinating, and automatic differentation in particular is becoming an amazingly powerful tool.

Magnetic excitations, non-classicality and quantum wake spin dynamics in the short-range Hubbard chain, by and Pontus Laurell, Allen Scheie, D. Alan Tennant, Satoshi Okamoto, Gonzalo Alvarez, Elbio Dagotto: This work asks the questions of how much information can be recovered from a quantum system of correlated electrons by looking at one- and two-point correlation functions, how these link to an experimentally measurable quantity known as the dynamical structure factor (DSF), and how these link to an entanglement measure known as the Quantum Fisher Information. In particular, the authors study a theoretical model known as the Hubbard model, a key tool in understanding a wide range of solid-state systems, and use these measures to investigate in detail the crossover from weakly-interacting to strongly-interacting behaviour. This opens the door to novel entanglement measures in correlated electron systems that to date, to my knowledge, have never been performed. I can’t help wondering whether similar measures would be possible using quench spectroscopy in ultracold atomic gases (something I’ve been involved in developing), extending the work done here in the solid-state context to the highly controllable ultracold atomic gas realm. Admittedly, this was not the goal of the authors of this work, but I’d never considered whether quench spectroscopy and entanglement could be related, and I’d be very curious to know the answer.

Mar 16th

Scaling of Fock-space propagator and multifractality across the many-body localization transition, by Jagannath Sutradhar, Soumi Ghosh, Sthitadhi Roy, David E. Logan, Subroto Mukerjee, and Sumilan Banerjee: The stability of the many-body localised phase, whether it even exists and the nature of the localisation phase transition are all key open questions in the field of disordered quantum systems which are, after a few years of slow going, finally starting to see some interesting progress. This work is a serious study of the localisation transition using a sophisticated Green’s function technique to study an analagous transition in a fictitious space known as a ‘Fock space’. The method itself is a bit too complex to get into here, but at its core it requires knowledge of all eigenstates of the system, which means that it falls back on exact diagonalisation methods, but nonetheless the information extracted from the numerics is quite comprehensive. The main finding here is further support for the idea that the many-body localisation transition is of Kosterlitz-Thouless type, in line with several other recent works using other methods which also come to the same conclusion. While I don’t think this scenario is definitively proven yet, it certainly seems increasingly likely.

Dynamical localization and many-body localization in periodically kicked quasiperiodic lattices, by Yu Zhang, Bozhen Zhou, Haiping Hu, and Shu Chen: The combination of (quasi)-disorder and periodic drive can lead to a variety of exotic behaviour, including the famous recent example of discrete time crystals. This work studies the interplay of (quasi)-disorder strength and drive frequency in order to characterise whether or not a localised phase exists. Broadly, the authors find that for large disorder strenths and high drive frequencies, localisation is stable, but if either of these are lowered far enough, the system will transition into a delocalised phase. (Similar results can be seen in my own work on driven, disordered systems.) The authors characterise the transitions in detail using exact numerics, and show the existence of a complex phase diagram as a function of disorder and drive strengths.

Locality optimization for parent Hamiltonians of Tensor Networks, by Giuliano Giudici, J. Ignacio Cirac, and Norbert Schuch: This one’s a bit out of my wheelhouse and I’m a little fuzzy on the details, but I include it here because it seems like a really interesting bit of work. Tensor networks are one of the most powerful numerical techniques in modern condensed matter physics, but there’s a lot more to them than simply using them as an efficient framework to do numerical DMRG calculations. They can also be used as an analytical language, in which tensor network states appear as exact ground states of so-called ‘parent Hamiltonians’. Constructing these parent Hamiltonians is not easy, as they are often extremely complex and may contain terms which act on a large number of lattice sites. This work is a step forward in constructing comparatively simple parent Hamiltonians for tensor network states, and the authors propose a new optimisation technique which allows them to find simpler parent Hamiltonians than other existing methods, while still being able to reproduce known optimal models in several particularly well-studied cases.

Mar 17th

Localization properties of the asymptotic density distribution of a one-dimensional disordered system, by Clément Hainaut, Jean-François Clément, Pascal Szriftgiser, Jean Claude Garreau, Adam Rançon, and Radu Chicireanu: In one spatial dimension, any non-interacting system will become Anderson localized by the presence of any concentration of disorder (though possibly with an extremely long localisation length!), leading to eigenstates which decay exponentially in space. This is well-known to researchers in the field, but I wasn’t aware that a consequence of this is that an initially narrow wave packet could expand in a disordered medium to reach a steady-state distribution that wasn’t exponential in space, but instead takes a more complicated form originally derived by Gogolin in 1976. This work experimentally proves Gogolin’s equation, using a very interesting form of dynamical localisation realised in a quantum kicked rotor model. This is a periodically driven system that can be shown to be equivalent to an Anderson model in momentum space, opening the door to a very different view on localisation than we typically study. I would have liked to have seen a more thorough discussion of the duality between dynamical localisation and ‘conventional’ real-space localisation, but I suspect this has been done in other works - I’ll be digging through the reference list of this paper to learn more about this intriguing phenomenon!

Mar 18th

Robust quantum many-body scars in lattice gauge theories, by Jad C. Halimeh, Luca Barbiero, Philipp Hauke, Fabian Grusdt, and Annabelle Bohrdt: Earlier this week we looked at localisation in lattice gauge theories, and now it’s the turn of quantum many-body scars! Scar states are special states of a model that behave differently to typical states, exhibiting unusually low entanglement entropy as well as other distinguishing features. In particular, if a system is initialised in a scar state, it will not thermalise at long times, in contrast to its behaviour if it were initialised in any other generic state. Scar states are believed to be finely-tuned states which could be unstable to external perturbations in many experimental systems, but this work sets out to use a concept known as gauge protection to enhance scar states and make them more robust. The authors show that this proposal works well in experimentally relevant systems and at experimentally relevant timescales, and so it’s likely that we’ll see further work building on this mechanism to enhance exotic non-thermal dynamics in a range of other quantum systems.

Emergence of isotropy and dynamic self-similarity in the birth of two-dimensional wave turbulence, by Maciej Gałka, Panagiotis Christodoulou, Martin Gazo, Andrey Karailiev, Nishant Dogra, Julian Schmitt, and Zoran Hadzibabic: Turbulence, which I’ll loosely define here as the chaotic flow of a fluid, is something I associate with fields including hydrodynamics, weather systems, solar physics and cosmology, but it’s not something I’d associate with quantum physics, simply because turbulence is hard enough to study without adding quantum mechanics on top of it. This work, however, sets out to study a turbulent wave cascade in a two-dimensional ultracold atomic gas, a highly controllable experimental setup that allows researchers to measure in detail the microscopic properties of the bosonic particles used in the experiment. By applying an anisotropic, time-periodic magnetic field to generate the dynamics, the authors observe the emergence of turbulence and present a variety of measurements to back up their assertion that what they see is indeed turbulence. This is not remotely my area of expertise, but it’s fascinating and I will be extremely interested to follow the development of this field, as being able to study turbulence in such a highly controlled quantum environment is to my knowledge something very new, with a lot of potential for further work and interesting discoveries.