View from the arXiv: Feb 14 - Feb 18 2022
A summary of new preprints appearing on arXiv during the week of Feb 14th to Feb 18th 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)
Engineered Dissipation for Quantum Information Science, by Patrick M. Harrington, Erich Mueller, and Kater Murch: Dissipation is something I’m familiar with in the context of open quantum systems, i.e. quantum models coupled to an environment to which they can lose energy or particles, but this review presents dissipation from a different point of view, namely as a tool for engineering various aspects of quantum information, including measurement, state preparation and even as a means of implementing quantum error correction. The review also highlights the quantum Zeno effect, whereby the dynamics of a system can be constrained through a process of repeated measurements, providing another way in which dissipation can be used to tailor the properties of a quantum system, rather than being a problematic issue to be minimised. This review opened by eyes to possible practical uses of dissipation, rather than it simply being a way to encode particle loss or coupling to a heat bath, and it contains some very interesting concepts.
Emergence of a superglass phase in the random hopping Bose-Hubbard model, by Anna M. Piekarska, and Tadeusz K. Kopeć: I spent a lot of my PhD studying the disordered Bose-Hubbard model, but as with most studies, my work focused on so-called ‘diagonal disorder’, which is when the chemical potential varies randomly from site to site in a way that can be engineered relatively easily using speckle potentials or similar random patterns of light. This study, on the other hand, considers off-diagonal disorder – or hopping disorder, if you prefer – and the result is the claimed ‘superglass’ phase, where both long-range superfluid order and glassy order coincide and compete with each other. This resembles the inhomogeneous superfluid seen in systems with diagonal disorder, however the analysis here is more sophisticated, and it definitely warrants reading in more detail on my part to understand this phase better, as it seems extremely interesting. (See also arXiv:2202.06610 which appeared on Feb 15th by the same authors on the same topic.)
Fundamental problems in statistical physics XIV: Lecture on Machine Learning, by Aurélien Decelle: Just a quick one here, but for anyone who’s interested in machine learning and has a background in statistical physics, this looks like a very nice, short review of some key concepts in machine learning as seen through the lens of many well-known concepts from statistical physics.
Violation of the fluctuation-dissipation theorem and effective temperatures in spin ice, by Valentin Raban, Ludovic Berthier, and Peter C. W. Holdsworth: Spin ices are similar in many ways to spin glasses (which I’ve talked about before), but as I understand it their behaviour is caused by geometric frustration rather than any built-in disorder. This frustration means that there is a large number of exactly degenerate states at low energy, which can lead to slow dynamics reminiscent of spin glasses1. In this work, the authors take this similarity quite literally, and apply some tools from the study of spin glasses to the study of spin ice based around a material known as dysprosium titanate. In particular, they look at the fluctuation-dissipation theorem (FDT), a property that links the linear response of a material to its correlation function via its temperature. Knowing both the correlation and response allows one to extract the effective temperature of a model, in other words. The FDT is not always obeyed, however, and in spin glasses the simple form of the FDT breaks down due to the hierarchy of different timescales and energy scales that give rise to the slow relaxation properties that characterise these models. The authors find similar behaviour here in a spin ice, albeit with less significant aging effects. This is an interesting study that makes me want to learn more about the similarities and differences between spin glasses and spin ices.
Quantum phase with coexisting localized, extended, and critical zones, by Yucheng Wang, Long Zhang, Wei Sun, and Xiong-Jun Liu: In many disordered quantum systems, we find that all possible eigenstates are either localized or delocalized: whichever option they pick, they all behave the same way. In some systems, we find what’s known as a ‘mobility edge’, where all eigenstates below some energy are localized, while all states above this critical energy are delocalized. (Almost as if the high energy states have ‘melted’ the localised phase away.) Sometimes we even find exotic phenomena like inverted mobility edges, or other strange behaviour. This work focuses on a model of non-interacting spinful fermions in a spin-dependent quasiperiodic potential, and aims to find a region of parameter space where the many-body spectrum includes localized states, delocalized states and even critical states which are on the boundary between both other types of behaviour. Frankly I’m not sure I’d call this a ‘phase’, as it’s really a study of the distribution of localised/delocalised/critical states in the energy spectrum of a rather exotic model, but the findings are interesting and suggest that tailoring of disorder potentials can lead to more exotic mobility edge structures than previously known. This in turn could have implications for the non-equilibrium dynamics, where initial states which overlap strongly with localised eigenstates would display localization behaviour, while initial states which strongly overlap with delocalised eigenstates would look ergodic. By tailoring the potential to produce particular structures of excited states, it may be possible to tune the non-equilibrium dynamics and localisation properties, which would be an interesting area for future study.
Equilibrium Fluctuations in Mean-field Disordered Models, by Giampaolo Folena, Giulio Biroli, Patrick Charbonneau, Yi Hu, and Francesco Zamponi: Despite decades of study, spin glasses remain an enigma in many ways. While the ‘basics’ are understood, getting much beyond that requires a huge amount of effort, deep understanding and clever insight. This work is a study of how fluctuations in spin glasses affect their properties. Many thermodynamic observables – such as temperature – are given by the average behaviour of a huge number of particles. Typically, most particles have almost the same behaviour, with only minor fluctuations away from the average value. At phase transitions, however, the fluctuations can become much larger, and they can have a dramatic effect on the properties of a material. In a glassy system, where there are a huge number of metastable states close in energy, the complexity is tamed by the use of ‘mean-field’ methods, which give the average behaviour of an infinitely large system. This work is a study of fluctuations around this average, how to compute them and what their effect may be on the physics of real glasses away from the mean-field limit.
Observation of a continuous time crystal, by Phatthamon Kongkhambut, Jim Skulte, Ludwig Mathey, Jayson G. Cosme, and Andreas Hemmerich, Hans Keßler: I expect this one to be controversial – everything about time crystals is – but I couldn’t not include it, as this could have quite a big impact on the field if it holds up to scrutiny. Time crystals are a state of matter which breaks time translation symmetry: essentially, they display some form of oscillations that go on forever. This is not perpetual motion, as it has been shown that the only way this can occur is if the system is continuously being fed energy, usually in the form of some sort of periodic drive (i.e. a time-varying electric or magnetic field). To date, time crystals that have been studied have all been discrete time crystals, which break some form of discrete symmetry, but Wilczek’s original time crystal prediction was for a continuous time crystal. This paper claims to be the first experimental realisation of a continuous time crystal, which – if true – will certainly be a landmark result!
Scrambling Dynamics and Out-of-Time Ordered Correlators in Quantum Many-Body Systems: a Tutorial, by Shenglong Xu, and Brian Swingle: I wrote recently about wanting a guide to quantum information for many-body theorists, and while this paper isn’t that, it’s not a million miles off. It serves as an introduction to a particular concept from quantum information, known as information scrambling, written from a many-body physics perspective. Loosely, scrambling is when information contained in some initial state of a system is lost over time and can no longer be recovered by a local measurement: the information becomes ‘spread out’ across the system, encoded only in highly non-local degrees of freedom, tangled up in a web of many-body physics from which it can only be recovered with great effort to the point where for all practical intents and purposes, the information is lost. In particular, this work shows how scrambling dynamics can be quantified through the use of out-of-time ordered correlators (known as OTOCs), a tool which is becoming more and more common in many-body physics. This paper contains a lot of things I don’t (yet!) understand, and I look forward to reading it in more detail as it looks extremely useful, informative and accessible.
Decimation technique for open quantum systems: a case study with driven-dissipative bosonic chains, by Álvaro Gómez-León, Tomás Ramos, Diego Porras, and Alejandro González-Tudela: Often when studying the non-equilibrium dynamics of a quantum system, we assume – sometimes without even commenting or acknowledging it – that the system is well isolated from its environment, and that the dynamics are perfectly unitary (i.e. reversible) and given by time evolution with the Hamiltonian of interest. In reality, systems are almost always able to exchange energy with their environment, even very weakly, and this means that the dynamics are not in fact perfectly unitary. The system may be able to lose energy or particles to its environment, a process we call dissipation. This is often ignored because it’s a hard problem, and many experiments these days are able to achieve sufficiently good isolation from external environments that we don’t always need to include it in our calculations, but this is not always true. In this work, the authors develop a new method for the study of dissipation based on a real-space decimation technique applied to lattice Green’s functions. To me, at least, this seems very novel and the technique looks to be quite powerful. It’s nice to see a new approach to such a challenging problem!
Localization and delocalization properties in quasi-periodically driven one-dimensional disordered system, by Hiroaki S. Yamada, and Kensuke S. Ikeda: This is a paper that I am both very intrigued to see and slightly frustrated by, as I’d had a very similar study in mind as a nice potential project for any new Masters students joining the group in the next year! The key idea here is that when a d-dimensional system is subject to a periodic drive of a single frequency, it behaves like a (d+1)-dimensional system, i.e. in one spatial dimension higher. So what happens if we drive a system with M different frequencies - does it behave like a (d+M)-dimensional system? The answer is yes, and the authors of this work investigate this effective dimensionality by studying an Anderson model, which does not have a delocalisation transition in d<3 in the absence of periodic drive. By taking a one-dimensional system and periodically driving it, the authors find that they can induce a delocalisation transition when the effective dimension is large enough. Not necessarily a surprise, but nonetheless a nice result!
Scalable spin squeezing from spontaneous breaking of a continuous symmetry, by Tommaso Comparin, Fabio Mezzacapo, Martin Robert-de-Saint-Vincent, and Tommaso Roscilde: In quantum optics, so-called ‘squeezed states’ play an important role. The term refers to states where the quantum uncertainty of an observable is low compared with some reference state, usually taken to be a coherent state of light. A similar concept can be applied to quantum spins, and leads to the idea of ‘spin squeezed states’ which have very minimal uncertainty in their spin configuration. Being able to accurately prepare and measure quantum states is an important feature of any future quantum technology, particularly those with metrological applications. This work proposes a new way to generate squeezed states based on the breaking of a continuous symmetry, allowing them to be made in systems with short-range couplings, which are commonly realised in many experimental platforms (e.g. ultracold atoms, trapped ions, etc). This work opens the way for squeezed spin states to become a much more common resource in quantum simulators and future quantum technologies.
I will be honest, I don’t fully appreciate all the differences between spin ice and spin glass and would love to hear from a spin ice expert who’d be willing to help me understand this. ↩︎