View from the arXiv: Feb 28 - Mar 4 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)

Feb 28th

The discrete random energy model and one step replica symmetry breaking, by Bernard Derrida, and Peter Mottishaw: The idea of replica symmetry breaking plays a key role in the physics of spin glasses, and was likely a large factor in the award of the 2021 Nobel Prize to Giorgio Parisi, but while the general idea behind it is now largely understood, many of its details are yet to be unravelled and it is still unknown precisely when this theory is valid. This paper studies a relatively simple (for a spin glass…!) model where replica symmetry breaking reproduces some of the correct features, but not others. Understanding when this approach breaks down can give valuable information as to what physics it does or does not capture, as well as providing further hints as to how the theory can be developed and extended in the near future. Spin glasses are a fascinating topic, and this is a very interesting work that probes the fundamentals of one of the most powerful and widely used theoretical frameworks in the field.

Emergent quantum state designs and biunitarity in dual-unitary circuit dynamics, by Pieter W. Claeys, and Austen Lamacraft: I’ve been seeing the phrase ‘dual-unitary circuits’ a lot recently (not least because my office-mate Ryotaro Suzuki works on them…!) and for a while now I’ve been wanting an excuse to sit down and learn what they are. Well, that day has come with the release of this fascinating paper. The general idea is that typical many-body quantum systems display chaotic behaviour in line with a framework known as ‘random matrix theory’ (which also plays a large role in localization/delocalization transitions that I work on). This chaotic behaviour renders many problems impossible to solve exactly, and so new approaches are needed. Dual-unitary circuits are a special class of models which can be solved: they exhibit a duality between space and time (hence the name), and allow a novel window into chaotic dynamics and thermalization. This paper considers how dual-unitary circuits are linked to so-called quantum state designs, something which I don’t understand well enough to describe in a succinct manner but definitely want to learn more about. (Also, as someone who’s only recently started to get to grip with TikZ, I bet the many nice figures in this paper took a long time to make…!)

Mar 1st

Entanglement spectrum and quantum phase diagram of the long-range XXZ chain, by J. T. Schneider, S. J. Thomson, and L. Sanchez-Palencia: Quantum entanglement is the language in which quantum many-body systems speak, and if we want to understand many-body quantum systems, we need to be able to understand entanglement properties. In this work, we look at several slightly unconventional entanglement measures, namely the geometric entanglement and the entanglement spectrum. The former can be efficiently computed using matrix product state methods and is able to probe phase transitions that other quantities cannot resolve, while the latter requires a little more interpretation but gives a more complete picture of entanglement. We study these quantities in a spin chain with long-range couplings, and find the surprising result that the entanglement properties exhibit a remarkable self-similar behaviour, such that the entanglement spectrum of the long-range model can (in some cases!) be mapped onto the entanglement spectrum of the short-range model using a straightforward rescaling. This doesn’t work for every observable, but it is nonetheless a surprising observation that could open the door to innovative future studies making use of the link between short- and long-range systems. (Full disclosure: this ia a bit of a shameless plug as I’m one of the authors, but frankly it’d be strange if I didn’t highlight a paper I’m on as one of my most interesting papers of the week.)

Measurement-induced power law negativity in an open monitored quantum circuit, by Zack Weinstein, Yimu Bao, and Ehud Altman: Continuing today’s theme of entanglement, here we look at another entanglement measure known as the negativity. In this work, the authors tackle the case of whether meaningful entanglement can be preserved in a system coupled to an external environment. Typically, this results in components of the system becoming entangled with the environment instead of with each other, leading to a loss of internal entanglement within teh system. Here, the authors study a model where this is almost guaranteed to happen (consisting of a random unitary circuit applied to a 1D chain of qubits with dephasing at the boundaries), but then add an extra ingredient: random projective measurements. By randomly measuring part of the system, the dynamics becomes non-unitary (read: non-reversible) and this changes the properties of its evolution quite significantly. In particular, the authors show that making random measurements at a suitable rate allows for a half-system negativity which scales like the cube root of the system size: this is far from zero, as would be expected in the absence of measurements. Too high a rate of measurement changes the dynamics yet further. This is an interesting contribution to the rapidly exploding field of non-unitary dynamcis and projective measurements, and something I’m very curious to know more about.

Mar 2nd

Origin of long-lived oscillations in a Rydberg-blockaded chain: Projected precession of a large pseudospin, by Keita Omiya, and Markus Müller: Quantum scars are a fascinating phenomenon where a certain small number of special states exhibit dynamical behaviour very different from all other possible states. In particular, when a quantum system is prepared in such a ‘scar’ state and allowed to evolve under its own dynamics, it exhibits persistent oscillations that take a long (sometimes infinitely so!) time to vanish. This work is a study of scar states in one of the most well-known models exhibiting these unusual dynamics (the PXP model), and the authors argue that they have constructed an approach which allows a detailed understanding of these states to be developed for the first time, as well as allowing various extensions and incorporating the findings of a large number of existing works. I’m not familiar enough with the state of the art in the field of quantum scars to say for sure whether the authors achieve the goal they claim, but it certainly looks like this paper is worth a detailed read at a later date!

Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks, by Marcel Rodekamp, Evan Berkowitz, Christoph Gäntgen, Stefan Krieg, Thomas Luu, and Johann Ostmeyer: One of the biggest problems with quantum Monte Carlo – itself one of the most successful and powerful numerical tools in condensed matter physics – is that for certain systems, it just doesn’t work. An issue known as the ‘sign problem’ occurs, which results in the method being unable to extract the true solution due to having to sum together many large terms of alternating positive and negative sign. Essentially it’s like a signal-to-noise problem, where the ‘static’ of these alternating sign terms is much larger than the signal that researchers are trying to extract. Of all the ways to reduce the severity of this problem, a neural network approach seems like quite an innovative solution, and not one I’ve seen before. This looks like a promising method for future quantum Monte Carlo calculations, if it can be made easy enough to use by other researchers and in other codebases.

Mar 3rd

Universal transport in periodically driven systems without long-lived quasiparticles, by Iliya Esin, Clemens Kuhlenkamp, Gil Refael, Erez Berg, Mark S. Rudner, and Netanel H. Lindner: In recent years, researchers have achieved such a high level of control and understanding of exotic quantum mechanical phenomena that it has become possible to use non-equilibrium dynamics to engineer features which don’t exist in equilibrium systems. This work considers the interplay between topology and out-of-equilibrium physics, in a novel system consisting of a chain of Sachdev-Ye-Kitaev (SYK) dots, which goes beyond existing work on a topic known as ‘universal charge transport’ and shows that this exotic phenomenon does not in fact require long-lived quasiparticle states as previously thought, but in fact still arises even in a system without long-lived quasiparticle excitions such as an SYK-like model. This is a very interesting and technically accomplished piece of work, that has important implications for future studies of novel topological phases in the present of periodic drive and other far from equlibrium effects.

Mar 4th

Field theory for zero temperature soft anharmonic spin glasses in a field, by Pierfrancesco Urbani: As I’ve written here many times before, spin glasses are highly complex phases of matter that – despite decades of intense study – still are not entirely understood. In particular, spin glasses are often studied in the ‘mean-field’ limit of infinitely many spatial dimensions, where the equations become possible to solve, but studying glasses in a finite-dimensional system remains an open challenge. (I speak from experience - I’m trying to do it numerically at the moment!) In this work, the author constructs a finite dimensional spin glass model and the corresponding field theory, which in the mean-field limit reduces to another established spin glass model. This is potentially a huge step in the study of spin glasses, as it allows finite dimensional effects to be studied systematically using perturbative methods, something that until now has been a major challenge. This could shed light on the nature of spin glasses in finite dimensional systems – I wonder if it can even be extended to low-dimensional quantum systems someday in the future?

Disorder-free localization with Stark gauge protection, by Haifeng Lang, Philipp Hauke, Johannes Knolle, Fabian Grusdt, and Jad C. Halimeh: It’s by now well known in the condensed matter community that it’s possible to prevent a quantum system from thermalising by adding disorder into it, perhaps in the form of chemical impurities or other types of randomness. Stark localization, on the other hand, occurs in non-disordered (translationally invariant) systems subject to a linear electric field, however this is a somewhat finely-tuned example of ergodicity breaking and may not be stable to various forms of perturbation, and in particular is not stable in the presence of so-called ‘gauge-breaking errors’. This work takes the idea of Stark localization and uses it as a jumping-off point to propose a new concept known as Stark gauge protection, which the authors argue can be used to enhance and/or stabilize disorder-free localization in a variety of experimentally relevant models. This is a very interesting step along the road of exotic localization effects in disorder-free models, and I’ll be interested to see how this is used in the future!

Quantum Entanglement in the Sachdev-Ye-Kitaev Model and its Generalizations, by Pengfei Zhang: The Sachdev-Ye-Kitaev model is a fully-connected, highly disordered model of Majorana fermions with no spatial structure (strongly related to the mean-field glass models mentioned above!) that exhibits extremely chaotic dynamical behaviour, and yet somehow is also exactly solvable in many limits. This peculiar model was introduced to understand the ‘strange metal’ phase seen in solid state models, but became well known for its connection to quantum gravity and black holes. This review nicely bridges the gap between the quantum world and the gravitational theories, surveying the role of entanglement (a purely quantum mechanical effect) and relating it to the equivalent gravitational theories and the wormholes that emerge. This is a comprehensive and well-written work that I look forward to reading it more detail later, as it’s far too long to fully read before posting this summary. My only gripe about it is that it’s made us realise that a plan we had for an exciting upcoming project may already have been done!