View from the arXiv: Jan 31- Feb 04 2022
A summary of new preprints appearing on arXiv during the week of Jan 31st to Feb 4th 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)
Barriers to Macroscopic Superfluidity and Insulation in a 2D Aubry-André Model, by Dean Johnstone, Patrik Öhberg, and Callum W. Duncan: Quasicrystals are a fascinating state of matter, exhibiting long-range order while simultaneously not having a periodic structure like a conventional crystal. The Aubry-André model has been exhaustively studied in one dimensional systems, originally non-interacting systems and more recently in the context of many-body localization (including by me - shameless plug!), and the ground state properties of the two dimensional bosonic Aubry-André model have been the subject of increasing experimental and theoretical attention. This work uses a Gutzwiller mean-field algorithm to study the zero temperature ground state properties of the Bose-Hubbard model subject to a quasiperiodic (Aubry-André) potential, and in particular investigates the interplay between insulating and conducting phases. Contrary to the Bose-Hubbard model with random disorder, where rare Griffiths regions can disproportionately influence the bulk properties of the material, the Aubry-André potential is entirely deterministic and does not have rare regions, but instead it exhibits ‘weak lines of modulation’, where thin lines of one phase run through another. This manifests here as the ‘weak superfluid’ and ‘weak Bose glass’ phases studied here. It would be extremely interesting to see whether future works using beyond-mean-field techniques (e.g. quantum Monte Carlo) will also find similar behaviour, as mean-field methods in Bose-Hubbard models tend to be qualitatively reliable but can often overestimate superfluid coherence.
Designing quantum many-body matter with conditional generative adversarial networks, by Rouven Koch, and Jose L. Lado: Finding modern numerical techniques capable of capturing the full complexity of many-body quantum systems is a hard challenge, and even moreso when we want to compute dynamical properties. This work considers the use of a ‘generative adversarial network’ (GAN) to investigate dynamical properties of many-body quantum systems. This is another interesting example of applying machine learning techniques to condensed matter physics, and while I remain a tad sceptical about data-driven vs first principles approaches, I can’t deny that the results here are quite compelling and point to a future where machine learning techniques and more conventional many-body numerical methods are routinely combined to obtain the best of both worlds.
Many-body localization in a quantum gas with long-range interaction and linear external potential, by I.V. Lukin, Yu.V. Slyusarenko, A.G. Sotnikov: The phenomenon of many-body localization (MBL) remains a highly active research topic, and two particularly interesting frontiers are the existence of MBL in disorder-free systems (often called Wannier-Stark MBL) and the stability of localization to the addition of long-range couplings. This work studies both, and examines the general phenomenon of disorder-free MBL in a variety of different systems with long-range couplings, including fermionic, bosonic and spin models. This is a substantial study, dealing with a wide variety of different theoretical tools and observables, and it provides nice evidence that Wannier-Stark MBL is in fact stable to the addition of long-range interactions in the form of density-density interactions (fermions) or an Sz-Sz interaction (spins). This matches previous work (including mine…second shameless plug this week, sorry!) which found that certain types of long-range couplings in disordered systems can even weakly enhance localization phenomena, while other types of long-range coupling can destroy it entirely. To my knowledge, this is the first time long-range couplings have been studied in a disorder-free context, making this an extremely interesting bit of work!
The Jaynes-Cummings model and its descendants, by Jonas Larson, and Th. K. Mavrogordatos: Where to start with this enormous 237 review article, being published as a full-fledged ebook by IOP Publishing? Well, if you’ve ever wanted to know anything at all about the Jaynes-Cummings model, it’s probably in here! The Jaynes-Cummings model is a deceptively simple model for light-matter interaction, yet hosts a vast array of rich physics, and serves as a jumping off point for other models of light-matter coupling. I can’t pretend to have read this in enough detail to write anything about it here, but I’m certainly going to try to read it in the future, as this is a fascinating topic I’ve so far not had the opportunity to learn very much about.
A critical look into Luttinger’s theorem, by Jan Skolimowski, and Michele Fabrizio: In a nutshell, Fermi liquid theory – proposed by Landau, naturally – states that in metals, single-particle excitations are smoothly connected to the many-body excitations, provided the interaction strength is turned on gradually. This is a famous theory in condensed matter physics, and provides a powerful window into the behaviour of strongly correlated metals. One consequence of this theory is Luttinger’s theorem, which relates the Fermi surface of the emergent quasiparticles to the electron filling fraction. Due to the connection between these two theorems, it’s widely believed that if the Fermi liquid theorem breaks down, then Luttinger’s theorem will follow. However, Luttinger’s theorem has been derived independently of Landau’s Fermi liquid picture, using a non-perturbative (i.e. likely more robust) technique. So why, in that case, does the failure of Fermi liquid theory imply the breakdown of Luttinger’s theorem? The authors of this work set out to address this intriguing question, and to my non-expert eye, largely succeed in doing so. One particularly interesting consequence is their prediction of a gapless, incompressible electronic phase of matter, an unusual combination of properties rarely seen outside of disorded systems such as the Bose glass. This is quite a technical work, but an extremely interesting one.
Superfluidity in the 1D Bose-Hubbard Model, by Thomas G. Kiely, and Erich J. Mueller: The Bose-Hubbard model in one dimension is an extremely widely studied model, yet despite the efforts devoted to understanding it, some aspects remain challenging. In particular, many aspects of its superfluidity require a great deal of numerical effort to compute. In contrast to quantum Monte Carlo, many modern methods based around tensor networks can struggle to extract detailed properties of the superfluid phase, as computing the superfluid stiffness typically involves long-range couplings (i.e. periodic or anti-periodic boundary conditions) which are numerically very costly. Coupled with finite system sizes which can make it difficult to cleanly extract the Luttinger parameter (hey, Luttinger’s showing up twice this week!), accurately identifying the superfluid transition is no mean feat. In this work, the authors review and characterise a wide range of properties of the superfluid phase, and focus on comparing two numerical techniques which work directly in the infinite system size limit, bypassing finite size effects and allowing accurate measurement of various properties of the superfluid phase.
Two short ones today, as I don’t know enough about either to be able to write about them in detail: the first is Quantum Kernel Function Expansion for Thermal Quantum Ensemble, by Hai Wang, Jue Nan, Xingze Qiu, and Xiaopeng Li, and the second Experimentally accessible scheme for a fractional Chern insulator in Rydberg atoms, by Sebastian Weber, Rukmani Bai, Nastasia Makki, Johannes Mögerle, Thierry Lahaye, Antoine Browaeys, Maria Daghofer, Nicolai Lang, and Hans Peter Büchler. Both out of my area of expertise, but might be interesting to others who know more about the topics!
Memory effects in the density-wave imbalance in delocalized disordered systems, by Paul Pöpperl, Igor V. Gornyi, and Alexander D. Mirlin: The localized phases of disordered systems get a lot of attention, in part because powerful techniques exist for the study of the strong-disorder limit. It’s widely established that localized systems exhibit a ‘memory’ of their initial conditions, as all forms of transport are strongly inhibited, while delocalized systems quickly relax to a featureless thermal state. In this work, the authors study a delocalized – but still disordered – system, and they show that the relaxation takes the form of a power-law, which is slower than might be expected, leading to the ‘memory effects’ of the title. This is a mostly analytical paper, focusing on both one- and two-dimensional systems, supplemented by numerical studies of non-interacting systems in two dimensions. A very neat bit of work!
Effects of Temperature and Magnetization on the Mott-Anderson Physics in one-dimensional Disordered Systems, by G. A. Canella, K. Zawadzki, and V. V. França: Localization in electronic systems can come either from disorder (Anderson localization, and similar mechanisms) or strong interactions (Mott localization). In between the limits of strong disorder and strong randomness lies an intermediate regime of Mott-Anderson physics, where elements of both mechanisms are at play. This work studies the interplay between Mott and Anderson localization, including the effects of non-zero temperature which ‘melts’ the localized phases, presenting evidence based on the entanglement structure and demonstrating that Anderson localization is more robust to thermal effects than Mott localization.