View from the arXiv: May 30 - Jun 3 2022

A summary of new preprints appearing on arXiv during the week of May 30th to June 3rd 2022

Welcome to ‘View from the arXiv’, where each week I’ll put together a short list of new preprints which have appeared on 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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 30th

Infinite-randomness criticality in monitored quantum dynamics with static disorder, by Aidan Zabalo, Justin H. Wilson, Michael J. Gullans, Romain Vasseur, Sarang Gopalakrishnan, David A. Huse, and J. H. Pixley: The concept of measurement-induced phase transitions has led to a lot of interest in so-called ‘hybrid’ dynamics, e.g. quantum systems that do not undergo unitary evolution with respect to a Hamiltonian, but also are not described by a Lindblad master equation of the sort used for dissipative systems. Instead, measurement-induced phase transitions occur in systems which follow a unitary evolution that is periodically interrupted by some sort of measurement, leading to dynamics that is neither unitary nor dissipative in the traditional sense. Remarkably, it turns out that when the measurement rate increases above some threshold, there is a phase transition in the growth of entanglement in the system (from a so-called volume law to an area law). This work studies measurement-induced phase transitions in a system with random disorder and a spatially varying measurement rate, where they find that the phase transition is broadened from a precise critical point into a wide Griffiths region where rare regions (which can be of anomalously high or low disorder) dominate the dynamics. The authors investigate this phenomenon through a field theoretic approach making use of real-space renormalisation group, which is an interesting way to look at monitored quantum dynamics that I haven’t seen before. The method is approximate and only valid in the limit of a large on-site Hilbert space dimension, so it would be interesting to see in the future how severe this approximation is and how widely the authors’ findings hold beyond this limit.

Numerical Simulations and Replica Symmetry Breaking, by V. Martin-Mayor, J. J. Ruiz-Lorenzo, B. Seoane, and A. P. Young: Spin glasses are fiendishly complicated to study, both analytically and computationally, and indeed the problem of finding the ground state of an Ising spin glass is known to be NP-complete (i.e. very difficult!). This work is a chapter of an upcoming book which summarises the progress on numerically studying spin glasses, and in particular focuses on the concept of replica symmetry breaking (which is linked to the presence of a large number of ‘almost equivalent’ spin configurations close in energy, but separated from each other by large energy barriers). This is a nice summary of the current state-of-the-art in the numerical simulations of spin glasses, and a good reference for anyone wanting to learn more about these concepts.

May 31st

Multipartite Entanglement in the Random Ising Chain, by Jay S. Zou, Helen S. Ansell, and István A. Kovács: Entanglement is the natural language of many-body quantum systems in one dimension (and perhaps also in others…!), so it’s important to continue developing our understanding of various different entanglement measures in a variety of different scenarios. Recently there has been increasing interest in entanglement measures that go beyond the commonly-used entanglement entropy, and this work looks at two more subtle entanglement measures known as the negativity and the mutual information in an Ising spin chain with random disorder. The main point of this paper is to show that in two different models which exhibit qualitatively similar properties (as measured by ‘standard’ entanglement probes, these multipartite entanglement measures are capable of revealing subtle differences that shed more light on how entanglement differs between these systems. This is an interesting step along the road towards a more complete picture of how different entanglement measures complement each other in many-body quantum matter.

Universality in Anderson localization on random graphs with varying connectivity, by Piotr Sierant, Maciej Lewenstein, and Antonello Scardicchio: Anderson localisation is a fundamental property of non-interacting quantum systems subject to disorder, where quantum interference effects can prevent the system from thermalising and ’lock’ it in a far-from-equilibrium non-thermal state. This paper studies Anderson localisation on exotic lattices known as random graphs with varying connectivity, e.g. lattices where each site is connected to a varying number of other sites. This may seem like a rather abstract mathematical problem, but it in fact has deep connections with models of many-body localisation, which is still a difficult problem that isn’t fully understood. The authors of this work investigate the existence of a strange phase intermediate between Anderson localised and fully delocalised, known as a ’non-ergodic delocalised’ phase, and present strong evidence that at disorder strengths too weak to fully localise the system, this strange intermediate phase can indeed emerge. It will be interesting to see in future work whether the connection between Anderson localisation on regular graphs and many-body localisation can be further strengthened and explored.

Towards near-term quantum simulation of materials, by Laura Clinton, Toby Cubitt, Brian Flynn, Filippo Maria Gambetta, Joel Klassen, Ashley Montanaro, Stephen Piddock, Raul A. Santos, and Evan Sheridan: The longer the paper, the shorter my summary usually is, and in the case of this monster 94-page paper I’m not going to get into a lot of detail! The main idea here is to explore a new algorithm for the quantum simulation of real materials that may be feasible for real-world quantum computers in the near future. I find this particularly interesting as the question of how to write an arbitrary Hamiltonian in terms of a quantum circuit is something that I’ve been giving a lot of thought to recently, and the techniques in this paper are interesting from that point of view. I’m not expert enough to say how realistic the claims in this paper are, but I found them interesting to read and think about!

Jun 1st

Incommensurate many-body localization in the presence of long-range hopping and single-particle mobility edge, by Ke Huang, DinhDuy Vu, Xiao Li, and S. Das Sarma: There are many works studying many-body localisation in disordered quantum systems, but one thing that a lot of them have in common is that they start from an Anderson localised non-interacting system and then add interactions on top of it. In particular, many of the most commonly-studied models exhibit Anderson localisation for all eigenstates, meaning that we know with confidence that all eigenstates of the non-interacting model are localised and any delocalisation we see in the many-body system must come from the interactions. This work studies many-body localisastion in a model which has a single-particle mobility edge, which means that not all single particle eigenstates are localised. This in turn means that the question of many-body localisation in such a model is much more complex, and this is the question studied here. The take-home message is that the physics of the many-body localised phase here is qualitatively differnt from the ‘conventional’ case when the interactions are strong, but at weak/intermediate interactions the localisation looks just like in models without a mobility edge. This implies that the single-particle mobility edge doesn’t necessarily imply anything about the many-body localisation, and that it is rather the different energy scales present in the problem that makes the key difference. The authors suggest their findings may also be relevant to models with longer-range hopping, and this is something I’d be very interested to see in future work.

Bridging Effective Field Theories and Generalized Hydrodynamics, by Frederik Møller, Sebastian Erne, Norbert J. Mauser, Jörg Schmiedmayer, and Igor E. Mazets: Understanding genuine quantum effects in low-dimensional systems is still a huge challenge in the fields of condensed matter and atomic physics. Mean-field approaches, which work well in high-dimensional models, break down in lower dimensions where quantum fluctuations play a more significant role. One method that works well in understanding the non-equilibrium dynamics of one-dimensional integrable quantum systems is known as generalised hydrodynamics, which I won’t explain here in detail but will simply note that it has been very successful. This work extends the hydrodynamical approach to include thermal fluctuations, which usually require some sort of effective field theory, and looks like a powerful step forward for an already valuable tool for the study of the dynamics of low-dimensional quantum systems.

Jun 2nd

Dynamical conductivity of disordered quantum chains, by Shintaro Takayoshi, and Thierry Giamarchi: The dynamics of many-body quantum systems subject to random disorder is a hard problem to solve, and this work presents a novel way of computing the dynamical conductivity in such systems. The main idea is that rather than simulating the real-time dynamics - which is difficult to compute at long times for generic systems - the quantity of interest is computed directly in frequency space using a modified matrix product state approach. This enables the authors to get a comprehensive look at transport in disordered quantum systems from a slightly different point of view that one might commonly see using other methods, and consequently go beyond other methods and push their numerical results into a regime accessible by experiments but not by many other numerical methods. It all looks solid, but it will certainly be interesting to see if future experiments validate the results presented here, or if there are any hidden limitations to the new approach presented here that aren’t yet clear.

Jun 3rd

Computer simulations of the glass transition and glassy materials, by Jean-Louis Barrat, and Ludovic Berthier: Apparently a paper in honour of the ‘International Year of Glass 2022’ (which is the first I’m hearing of it!), this paper is a nice overview of the challenges in computationally simulating glassy systems, and with a different focus to the paper about numerical simulations of replica symmetry breaking featured earlier this week. Glasses exhibit an extremely slow relaxation towards thermal equilibrium, due to their immensely complex structure, and so it can be challenging to simulate long enough time scales to really say anything concrete about their behaviour, except in specific cases where mean-field solutions exist (here I’m thinking of the Keldysh formalism for fully-connected spin glasses). This paper gives a good high-level overview of the techniques developed to overcome some of the challenges, and a perspective on the current state-of-the-art and where the field may go in the near future. One interesting thing I would’ve liked to have seen more of is a look at whether there’s much interplay between modern machine learning techniques and the solution of physical glass problems, as mathematically these fields have a lot in common and I wonder how deep this connection goes?

Resource-Efficient Quantum Simulation of Lattice Gauge Theories in Arbitrary Dimensions: Solving for Gauss’ Law and Fermion Elimination, by Tomer Greenberg, Guy Pardo, Aryeh Fortinsky, and Erez Zohar: Lattice gauge theories are something I know little about, but have recently been becoming more and more interested in. They are deeply related to fundamental questions – the example of an important gauge theory used in this paper is quantum chromodynamics and the strong nuclear force – and extremely difficult to solve or simulate using conventional methods. Quantum simulation, then, is potentially an extremely useful tool that could shed some light on gauge theories: finding a many-body quantum system that realises one of these gauge theories is an important goal, so that they can be simulated and experimented on in laboratory conditions. The problem is that many gauge theories translate to highly complex many-body systems that are difficult to simulate, either numerically or experimentally. This paper presents a potential way of making the connection to experiments in a simpler fashion, making it easier for future experiments to simulate lattice gauge theories. The details are a little over my head, but this looks like an interesting bit of work that could have significant impact in the field of quantum simulation, and open up new possibilities for what simulators can be used to investigate.

Dr Steven J. Thomson
Dr Steven J. Thomson
Research Scientist at IBM Research

Theoretical condensed matter physicist, currently a Research Scientist at IBM Research UK.