# View from the arXiv: Jan 17-21 2022

A summary of new preprints appearing on arXiv during the week of Jan 17th to Jan 21st 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)

**Jan 17th**

*Localization and multifractal properties of the long-range Kitaev chain in the presence of an Aubry-André-Harper modulation by Joana Fraxanet, Utso Bhattacharya, Tobias Grass, Maciej Lewenstein, and Alexandre Dauphin*: The title is a bit of a mouthful, but this paper combines a remarkable number of concepts all in one place! Localization, multifractality, long-range interactions, the Kitaev model *and* a quasiperiodic Aubry-André-Harper potential? Talk about an ambitious collection of topics! Although the model itself is non-interacting (i.e. quadratic in terms of fermion modes), this deceptively simple-looking Hamiltnian given in Eq. 1 of this paper gives rise to a fascinating array of behaviour. The authors study the interplay of long-range fermionic hopping with a long-range superconducting pairing term, all set against the backdrop of a quasi-random local potential. They find that the outcome of all these ingredients is a model with unusual localization properties, including the hybridization of bands with different localization characteristics and the emergence of two different multifractal regimes.

*Bond order via cavity-mediated interactions by Titas Chanda, Rebecca Kraus, Jakub Zakrzewski, and Giovanna Morigi*: Another highly interesting work from the prolific Zakrzewski group - I don’t know how they turn out so many great papers on such a regular basis! In this work, they study a Bose-Hubbard model in the context of cavity quantum electrodynamics, where dissipative couplings between the bosons and the cavity modes lead to new effective bosonic interactions (the ‘cavity-mediated interactions’ of the title) which take the form of both density-density interactions and correlated hopping processes. Using a numerical approach based around density matrix renormalization group (DMRG), the authors calculate phase diagrams at a variety of filling fractions and show that the cavity-mediated interactions can lead to the formation of new phases not present in the bare Bose-Hubbard model (known as Bond Superfluid, Bond Supersolid and Bond Insulator phases). This work shows how light-matter coupling can allow the engineering of novel Hamiltonians which can stabilize unusual phases, and will surely lead to more work studying similar effects.

**Jan 18th**

– No mailing list today! –

**Jan 19th**

*Geometry of rare regions behind Griffiths singularities in random quantum magnets by István A. Kovács, and Ferenc Iglói*: The addition of disorder in a quantum system can lead to a variety of effects. Close to a phase transition, it can modify critical exponents, or even smear out a sharp phase transition into a broad crossover region. In extreme cases, so-called Griffiths phases can occur, where due to the disorder small patches of the system can appear in the ‘wrong’ phase close to a phase transition. For example, in a disordered magnet such as the authors of this paper study, anomalously strong couplings between spins can lead to the emergence of small, locally ferromagnetic clusters even in what should be the paramagnetic phase. The existence of these rare regions can completely change the thermodynamics of the system, and indeed this is something I worked on a lot in my PhD studies. In this work, the authors study the geometric structure of rare regions in both dilute and fully random spin chains using strong disorder renormalisation group, which sheds some light on how the regions are distributed and how their properties are connected.

*Hamiltonian engineering of spin-orbit coupled fermions in a Wannier-Stark optical lattice clock by Alexander Aeppli, Anjun Chu, Tobias Bothwell, Colin J. Kennedy, Dhruv Kedar, Peiru He, Ana Maria Rey, and Jun Ye*: Wannier-Stark localization is a peculiar effect whereby a disorder-free system can exhibit localization phenomena due simply to a linear potential gradient, e.g. a ’tilt’ of the lattice. In this work, the authors show experimentally that a fermions in gravity-tilted shallow lattice together with spin-orbit coupling can lead to a very stable system which can be used to realise an extremely accurate optical lattice clock with excellent precision and coherence properties. This is an impressive result, and an intriguing further step in the development of quantum metrology.

**Jan 20th**

*Simulating chiral spin liquids with projected entangled-pair states, by Juraj Hasik, Maarten Van Damme, Didier Poilblanc, and Laurens Vanderstraeten*: The ongoing development of tensor network states in two dimensions in the form of projected entangled pair states (PEPS) is an area of rapid progress, but also a field facing a lot of challenges. In particular, it is important to characterise exactly what sorts of physics can be captured by the PEPS ansatz, and what escapes it. This is a fascinating work showing that PEPS methods can indeed capture the chiral edge modes of a chiral spin liquid phase, showing that PEPS methods have a promising future for the study of chiral topological order. (With thanks to Dr Augustine Kshetrimayum for highlighting this study and its importance in our work Slack chat.)

**Jan 21st**

*Localization of matter waves in lattice systems with moving disorder, by Chenyue Guo, and Zi Cai*: I’ve been interested in disordered systems ever since the start of my PhD, but the majority of studies look at so-called ‘quenched’ disorder, where the randomness is static, unmoving and unchanging. In this work the authors study a time-dependent random potential, where the disorder changes over time in a non-periodic way, such that the system is neither a standard Anderson insulator nor an example of a periodically driven Floquet system. I’m not sure what physical systems this description is relevant to, but I’d be very excited to see experiments using ultracold atomic gases and trapped ions try to realise some of this physics - I have no real intuition for how dynamic disorder behaves, but from a fundamental point of view it’s very intriguing.

*Suppression of inter-band heating for random driving, by Hongzheng Zhao, Johannes Knolle, Roderich Moessner, and Florian Mintert*: Continuing the theme of non-trivial dynamics, this paper considers the Bose-Hubbard model which can be realised in ultracold atomic gases (as well as certain solid state magnetic systems), and examines what happens in the case of ‘random multipolar driving’, a drive protocol which interpolates between fully random and quasi-periodic drive. The authors show that heating between energy bands can be suppressed by specific choices of drive, allowing for the existence of long-lived, relatively stable non-equilibrium states known as ‘prethermal states’. These states are, according to this study, accessible by current experiments, and so this random drive protocol proposed here may very soon allow the experimental realisation of novel non-equilibrium states in ultracold atoms labs, and in particular might allow these states to be investigated in two or higher dimensions, a regime currently out of reach of theoretical/numerical methods.