# View from the arXiv: May 16 - May 20 2022

A summary of new preprints appearing on arXiv during the week of May 16th to May 20th 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)

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**May 16th**

*Thermalization of interacting quasi-one-dimensional systems, by Miłosz Panfil, Sarang Gopalakrishnan, and Robert M. Konik*: One of the main frontiers in modern condensed matter and atomic physics is establishing how a quantum system prepared in an arbitary state eventually approaches – or fails to approach – thermal equilibrium. Often this is studied in isolated one-dimensional models, but many experiments (particularly ultracold atomic gases) instead consist of arrays of one-dimensional chains which are weakly coupled together, spoiling the perfect isolation of the one-dimensional chains. Understanding how the weak coupling between the chains affects the thermalisation properties is therefore extremely important. One interesting finding in this work is the existence of a family of thermalisation timescales, reminiscent in some ways of what can be seen in disordered or glassy systems, as well as the development of an analytical Boltzmann equation formalism which allows the thermalisation process to be understood in great detail.

**May 17th**

*Dynamical emergence of a Kosterlitz-Thouless transition in a disordered Bose gas following a quench, by Thibault Scoquart, Dominique Delande, and Nicolas Cherroret*: The question of understanding how many-body systems relax towards equilibrium appears again in our second paper this week, here in a two-dimensional bosonic gas initially prepared in a plane-wave state and then evolved subject to a disordered on-site potential. The authors find that at weak disorder and low temperature, the system relaxes to a superfluid state with algebraic (i.e. long range) correlations, while for strong disorder and/or higher temperatures, the system relaxes towards a normal fluid state with exponentially decaying correlations. Inbetween both limits, the authors propose a phase transition of Kosterlitz-Thouless type. It would be interesting to see how this would look in a lattice model where other phaess (the Bose glass and Mott insulator) could also exist, and whether this could lead to even richer non-equilibrium behaviour following a quench of the disorder potential.

*Emergent spacetimes from Hermitian and non-Hermitian quantum dynamics, by Chenwei Lv, and Qi Zhou*: A lot of this paper is over my head, but it touches on some deep fundamental issues so I thought it was worth including here. The idea is to see how the dynamical evolution of a quantum system can be expressed in terms of an emergent spacetime metric, e.g. an equation that describes the structure of spacetime. The idea, if I understand rightly, is to associate the optimisation of quantum circuit dynamics with the question of calculating geodesics (the shortest line connecting two points) in the equivalent spacetime, thereby connecting the dynamics of a quantum system with the concept of trajectories in exotic spacetime geometries. It’s an interesting idea, and certainly worth thinking about.

**May 18th**

*Nonequilibrium dynamics of the localization-delocalization transition in non-Hermitian Aubry-André model, by Liang-Jun Zhai, Guang-Yao Huang, and Shuai Yin*: In quantum mechanics, we normally work with models described by Hermitian operators, which results in (for example) systems whose energy is conserved over time. Non-Hermitian models have recently begun to attract a lot of attention because they allow the study of systems *without* energy conservation (e.g. allowing for dissipation/loss, encoded in eigenvalues which do not have to be purely real) using a Hamiltonian framework without having to use much more complex methods such as the Lindblad master equation approach. In particular, the combination of non-Hermitian Hamiltonians and disorder gives rise to a neat way of investigating the stability of localised phases to dissipation and loss, and that’s what’s studied here in a quasiperiodic Aubry-André model with direction-dependent hopping. They investigate the static properties, and also see what happens when the system is dynamically tuned through the critical point. They find that the response of the system exhibits Kibble-Zurek scaling, as might be expected in the corresponding Hermitian system, but which has not (to my knowledge) been studied in non-Hermitian models of this type.

*Discrete time crystals enforced by Floquet-Bloch scars, by Biao Huang, Tsz-Him Leung, Dan Stamper-Kurn, and W. Vincent Liu*: Time crystals have become a hugely active topic of research, and understanding the way in which time crystals connect to other forms of ergodicity breaking in quantum systems is one of the main goals of the field. This work connects discrete time crystal behaviour with quantum many-body scars, with the goal of showing how the existence of scar states in periodically driven systems can stabilise time crystal behaviour. This model is quite finely tuned, relying on a so-called trimerized kagome lattice structure and various other specific features, but nonetheless gives rise to an analytically tractable system that exhibits very intriguing non-ergodic properties, and potentially points towards some very interesting future research directions that build on the steps taken in this work.

**May 19th**

*Comment on “Universal and Non-Universal Correction Terms of Bose Gases in Dilute Region: A Quantum Monte Carlo Study’’, by Adam Rançon*: I’ve included this one less because of the physics included, and more because I can’t recall the last time I saw a ‘Comment’ article that was this constructive and respectful. Often ‘Comments’ are used to criticise or point out errors in work, which in turn can lead to a ‘Reply to Comment’ response from the original authors and a bitter public feud. This paper simply points out that some results in a recently published paper can be obtained in another (analytical) way, and shows that this method provides consistent results and a complimentary insight to the original paper. I won’t go into the physics here, but I wanted to flag this as a nice, responsible piece of work of a type that I don’t see nearly enough of. Props to the author for this one!

*Quantum simulation of ℤ2 lattice gauge theories with dynamical matter from two-body interactions in (2+1)D, by Lukas Homeier, Annabelle Bohrdt, Simon Linsel, Eugene Demler, Jad C. Halimeh, and Fabian Grusdt*: The study of lattice gauge theories is perhaps more commonly associated with high-energy physics than condensed matter, but recent advances in the degree of experimental control made possible by the latest generation of quantum simulators have brought them into the realm of condensed matter and atomic physics. They still remain challenging to experimentally study, however, as a key ingredient of lattice gauge theories is the presence of a form of local constraint on the Hilbert space which can be formulated in terms of Gauss’ law. Enforcing this constraint experimentally is where the difficulty lies: this work proposes a new way of protecting this constraint in current experimental platforms, at least up to experimentally relevant timescales, potentially opening the way for the investigation of a wide variety of novel physics (including disorder-free localisation!) in near-future experiments.

**May 20th**

*Exact mobility edges in Aubry-André-Harper models with relative phases, by Xiaoming Cai, and Yi-Cong Yu*: The Aubry-André-Harper (AAH) model is an intriguing system that is intermediate between translationally-invariant and disordered systems, characterised by a deterministic but not translationally invariant on-site potential, known as ‘quasiperiodic’. Variations of the model have been studied recently which exhibit a property known as a mobility edge, which means that certain eigenstates are below a certain energy are localised, while states above that energy are delocalised. This paper analytically studies a model from the AAH family, and the authors analytically calculate the mobility edge and various other localisation properties. It’s rare to see a model exhibiting localisation which is amenable to this sort of exact treatment, making this an interesting piece of work.