# View from the arXiv: Apr 11 - Apr 15 2022

A summary of new preprints appearing on arXiv during the week of Apr 11th to Apr 15th 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)

**Apr 11th**

*A note on the quasiperiodic many-body localization transition in dimension d>1, by Utkarsh Agrawal, Romain Vasseur, and Sarang Gopalakrishnan*: The stability of the many-body localized (MBL) phase in one-dimensional systems with random disorder has recently come into question, with a variety of works suggesting that the phase is not as stable as originally suspected, while others suggest the contrary. Many other works consider *quasiperiodic* systems, however, which are intermediate between fully random systems and perfectly translationally invariant systems, yet MBL is on a less firm footing in such systems even in one dimension, although many works indicate that a stable MBL phase exists in this regime. This work bypasses one dimension entirely and skips straight to two dimensions, making the argument that a localized phase may be stable in a two dimensional quasiperiodic system. The argument hinges on events known as *resonances*. A resonance occurs when it is energetically favorable for a particle to move from one lattice site to another: a large number of resonances mean that particles are free to move throughout a system, and therefore the particles are said to be delocalized. In contrast, a small number of resonances can mean that particles are forbidden from moving and as such are *localized*. This paper makes the case that the deterministic structure of resonances in quasiperiodic systems (something I’ve also investigated recently) mean that in two dimensions, resonances are prevented from proliferating throughout the system and causing delocalization. The argument here is that the MBL phase in 2D quasiperiodic systems is stable to the established argument for delocalization via resonances (known as the ‘avalanche argument’), but the authors are quick to volunteer that there could be other instabilities not captured in their analysis which could modify their conclusions. An interesting work, and one of a small (but ever increasing!) number of works to study many-body localization in two dimensions.

*Modern applications of machine learning in quantum sciences, by Anna Dawid, Julian Arnold, Borja Requena, Alexander Gresch, Marcin Płodzień, Kaelan Donatella, Kim Nicoli, Paolo Stornati, Rouven Koch, Miriam Büttner, Robert Okuła, Gorka Muñoz-Gil, Rodrigo A. Vargas-Hernández, Alba Cervera-Lierta, Juan Carrasquilla, Vedran Dunjko, Marylou Gabrié, Patrick Huembeli, Evert van Nieuwenburg, Filippo Vicentini, Lei Wang, Sebastian J. Wetzel, Giuseppe Carleo, Eliška Greplová, Roman Krems, Florian Marquardt, Michał Tomza, Maciej Lewenstein, and Alexandre Dauphin*: This is an extremely long (268 pages!) set of lecture notes that serves as a comprehensive introduction to machine learning and its uses in quantum physics and quantum chemistry. Its contents are far too long to get into here, but if I understand the conclusion correctly this is the result of a collaborative effort between lecturers and participants of a machine learning conference hosted in Warsaw late in 2021, which is a really nice origin story for this impressive and interesting bit of work.

**Apr 12th**

*Coexistence of localization and transport in many-body two-dimensional Aubry-André models, by Antonio Štrkalj, Elmer V. H. Doggen, and Claudio Castelnovo*: Hot on the heels of yesterday’s work arguing for the stability of many-body localisation (MBL) in two-dimensional quasiperiodic systems, here comes *another* paper making the same claim but from a different point of view. This paper studies hard-core bosons in rectangular-shaped two-dimensional systems, and presents evidence for a long-lived localised phase through a combination of numerical simulations and physical insights. The main idea here is that, as in yesterday’s work, rare regions are absent in quasiperiodic potentials and the structure of the resonances which lead to delocalisation is deterministic and predictable. Rather than arguing on a statistical basis that the resonances cannot proliferate, this work instead shows that the main consequence of the structured periodic potential is that it leads to what the authors call ’lines of weak potential’, which are effectively channels through the system that allow for particle transport even though the majority of the system is localised - think of the tunnels in an ant farm, for example, if you want to picture these conducting channels in an otherwise insulating background. The idea is that these lines allow a limited form of transport, but they cut the system into a large number of effectively disconnected regions which do not thermalise, leading to a coexistence of localised and thermalised regions within a single sample. This work reminds me of some previous work on the Bose glass phase in quasiperiodic systems which also provided evidence for unusual low-disorder lines which allowed for transport, despite large ‘islands’ of the system being trapped and unable to thermalise, and it seems that the main advance in the new work is to extend this logic away from the ground state and show that even for excited states, these rare lines of weak potential are not sufficient to lead to thermalisation of the full system.

*Enriching the quantum toolbox of ultracold molecules with Rydberg atoms, by Kenneth Wang, Conner P. Williams, Lewis R.B. Picard, Norman Y. Yao, and Kang-Kuen Ni*: The intersection between condensed matter, atomic physics and quantum information is fascinating, but often researchers from the different communities speak in a very different language from one another, and trying to find papers that translate quantum information concepts into concrete experimental frameworks (and vice-versa) can be a bit of a challenge. This is one of those rare works that combines quantum information theory with a very precise experimental protocol that looks very intriguing. The context is that while there are now many promising experimental platforms for quantum computing, it’s still difficult to perform computational operations in real systems without errors and noise creeping in and ruining things. There are some proposals for ways to correct errors and avoid noise, but these rely on slow processes which are difficult to implement in current generation experiments. This work proposes a modified experimental setup using Rydberg atoms which the authors show is capable not only of accurately performing computational operations, but can do so much faster than previous proposals, meaning that it’s potentially far more feasible in near-term quantum computers and therefore could be a very useful development. The authors don’t present this as a revolutionary step, but as simply one more tool that can be added to the box of tricks that experimenters building quantum computers can make use of in designing real devices for quantum computing.

**Apr 13th**

*Density Matrix Renormalization Group with Tensor Processing Units, by Martin Ganahl, Jackson Beall, Markus Hauru, Adam G. M. Lewis, Jae Hyeon Yoo, Yijian Zou, and Guifre Vidal*: The density matrix renormalization group (DMRG) is one of the central numerical techniques used in modern quantum condensed matter physics, particularly in one-dimensional systems as it provides an efficient way to encode the most significant information about a quantum system in only a (relatively) small number of parameters. It is usually now understood in the language of matrix product states, where a given quantum state can be expressed in terms of a product of matrices. The size of each matrix – and the number of variational parameters contained within it – is controlled by a number known as the bond dimension, which is typically ~10^2 for systems of a few hundred lattice sites (YMMV). This work makes use of Google’s state of the art Tensor Processing Units (TPUs), which are highly optimised processors for fast matrix algebra, and studies the challenging case of two dimensional systems. The authors manage to reach bond dimensions of 2^16 – that’s 65,536 – which is incredibly large compared to conventional simulations, albeit the models considered (free fermions and the transverse field Ising model) both have representations in terms of non-interacting fermions, so I’m not clear on how this method would perform for even more complex systems. Still, purely in practical terms, a bond dimension this large is an amazing achievement and really marks TPUs as an incredible bit of hardware for future simulations of quantum systems.

*Controlling topological phases of matter with quantum light, by Olesia Dmytruk, and Marco Schirò*: The interaction between light and matter in quantum systems is a fascinating area of ongoing research, where exotic states of matter can be stabilised by coupling a quantum system to some form of light field in the form of periodic drive or some sort of optical cavity (known as cavity quantum electrodynamics). This work looks at how the topological properties of quantum mechanical models can be influenced by cavity modes, quantum mechanical descriptions of light bouncing back and forth within a highly reflective cavity. In particular, the authors show that topologically trivial models (i.e. those with no interesting topological properties) can become topologically non-trivial once they are coupled to the quantum light field of the reflective cavity, characterised by the existence of so-called *edge modes*. This is a really interesting work that potentially opens a new route towards controlling the topological properties of quantum matter using light, and it’ll be interesting to see how this is built upon in the future. (Full disclosure: I have worked closely with Marco Schiró, one of the authors of this work, for several years, including on another paper that came out this week.)

**Apr 14th**

*Are fast scramblers good thermal baths?, by Ancel Larzul, Steven J. Thomson, and M. Schiro*: The Sachdev-Ye-Kitaev models is an example of a ‘fast scrambler’, which is to say that it’s a quantum system that thermalises as fast as possible following a quench out of equilibrium. It’s a well-studied paradigm of quantum chaos, with links to black holes and quantum gravity, but its the fast scrambling properties of the model that we’re interested in here. The question is whether the extremely fast thermalisation rate of an SYK model would mean that it’s also good at thermalising any other system it is brought into contact with. It turns out that the answer is ‘yes’! In the regime of weak system-bath coupling, the conventional SYK model (which we call the SYK4 model) is more efficient at thermalising a coupled system than a more conventional bath made of non-interacting degrees of freedom (which we model by a quadratic so-called SYK2 model). We trace this back to the enhanced density of states of the SYK4 model at low frequencies, as compared to a conventional thermal bath. At strong coupling, however, the performance of the SYK4 and SYK2 models is almost identical, and both baths lead to the system evolving in a similar way and on a similar timescale. (Conflict of interest statement: I’m one of the authors…!)

*Near-Equilibrium Approach to Transport in Complex Sachdev-Ye-Kitaev Models, by Cristian Zanoci, and Brian Swingle*: The second SYK paper in a single day, and I’ve got to admit I was a lot more conflicted about this one, as though the work is extremely interesting, we were actually working on a very similar thing here in Berlin! So while the emergence of this work might force us to adapt and change our plans a little, I have to say that I find this extremely interesting. The idea is to look at a one-dimensional chain of coupled SYK ‘atoms’ and examine their transport properties, which turns out to be analytically tractable in certain limits despite the strongly interacting (and highly complex!) nature of the model. This particular work is quite technical in nature, but it contains a lot of insight and careful analysis, and I suspect that some of the tools developed here will see a great deal of use in the near future.

*A Decade of Time Crystals: Quo Vadis?, by Peter Hannaford, and Krzysztof Sacha*: Time crystals, first predicted in Frank Wilczek in 2012, have been a reality now for several years. This paper reviews the developments that have occurred since Wilczek’s original idea, how the original idea didn’t work and had to be modified, the original experiments that first uncovered this physics and the ever-increasing number of new avenues of investigation motivated by this bizarre phenomenon. This is a fairly brief and very readable summary of how the field has evolved over the years and the current state of the art, so rather than say much more, I’ll simply encourage you to read this paper if you’re interested in time crystals.

**Apr 15th**

*Floquet-heating-induced non-equilibrium Bose condensation in an open optical lattice, by Alexander Schnell, Ling-Na Wu, Artur Widera, and André Eckardt*: Bose condensation is a phenomenon that occurs when a macroscopic (i.e. large!) number of bosons all occupy the same quantum state, which is typically the ground state of a system at very low temperature. Floquet heating, by contrast, is what happens when a generic system is subject to a periodic drive (i.e. it’s ‘shaken’), as the system normally absorbs energy from the drive and heats up. This work combines both, and shows that a driven system of bosons coupled to a thermal bath can exhibit a non-equilibrium Bose condensation, where the condensate is not in the ground state of the un-driven system but is instead balanced on a knife-edge where neither the periodic drive nor the dissipation due to a thermal bath is able to destroy it. This is another work to add to the collection of systems where non-equilibrium effects can be exploited to stabilise new phases of matter, and hopefully we’ll see this realised in experiments soon.