View from the arXiv: Mar 21 - Mar 25 2022
A summary of new preprints appearing on arXiv during the week of Mar 21st to Mar 25th 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 As these are all preprints which have not yet been peer-reviewed, remember to take any claims and conclusions with a grain of salt and be sure to cast a critical eye over the work if you’re interested in more details.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…!)
Nested Iterative Shift-invert Diagonalization for Many-body Localization in the Random-field Heisenberg Chain, by Taito Kutsuzawa, and Synge Todo: The detailed study of many-body localization still constitutes a significant numerical challenge, as it requires full knowledge of all eigenstates of a system, meaning that full exact diagonalization is the only numerical method that can give full information about the phase. This work develops a variant of the shift-invert technique that runs on a GPU, potentially allowing access to large system sizes without requiring a supercomputer. In addition, it proposes a new measure of the localization called a ’twist operator’ which should have an expectation value of zero in a thermal phase, and be non-zero in a localized phase. Using this, and a linear extrapolation to large system sizes, the authors argue that the localisation transition takes place at a larger disorder strength than previously reported, in line with other recent work providing similar evidence. Interestingly, the raw data presented in this work looks to be consistent with previous estimates of the critical disorder strength being h=3.7, but the linear extrapolation is more in line with a higher estimate of h~5.4, suggesting that finite size effects are still significant even for state-of-the-art numerical methods.
Quantum boomerang effect in systems without time reversal symmetry, by Jakub Janarek, Benoît Grémaud, Jakub Zakrzewski, and Dominique Delande: When studying disordered quantum systems, there are two main approaches that we often take. One is to focus on the static properties of the system (eigenvalues, eigenstates and so on), and the other is to look at the non-equilibrium dynamics following a some form of quench. The authors of this paper take a different approach, instead studying what happens to an already-moving wave packet in a disordered potential. In systems with a symmetry known as time-reversal invariance, it’s known that a moving particle exhibits an effect called the quantum boomerang effect, which says that the wavepacket will always return to its initial position. Previous works relied on time-reversal symmetry in order to explain the effect: here, the authors show that the quantum boomerang effect still persists even when time-reversal invariance is broken, and they offer a combination of numerical evidence and an analytical argument in order to demonstrate their findings.
Emulating Quantum Dynamics with Neural Networks via Knowledge Distillation, by Yu Yao, Chao Cao, Stephan Haas, Mahak Agarwal, Divyam Khanna, and Marcin Abram: The combination of neural networks and traditional condensed matter problems is a fascinating area of ongoing research, and this work is an interesting contribution to the field. Rather than simply being a case of using machine learning techniques to generate data and then analysing it, this paper takes a deep look at how neural networks can learn, and how this can be analysed to lead researchers to the discovery of new insights, such as fundamental relations between input parameters. The authors also study how the neural network performs at predicting the behaviour of systems not included in the training data. I’m particularly interested in the capability of a neural network to be trained on a simple dataset, but then be (successfully!) applied to more complicated general cases. This work is increasing my desire to start playing with machine learning techniques in my own research…!
The randomized measurement toolbox, by Andreas Elben, Steven T. Flammia, Hsin-Yuan Huang, Richard Kueng, John Preskill, Benoît Vermersch, and Peter Zoller: I work in a group where a lot of people study ‘random measurements’ and I have to admit that until I saw this paper, I had no idea what that phrase actually meant. The idea, as I understand it, is that randomised measurements can be a particularly efficient way to reconstruct a reasonably complete picture of a given quantum state. One aspect I found quite interesting is that random measurements give access not only to local observables (which doesn’t seem too far-fetched), but also to properties of the density matrix, which surprised me. All in all, I don’t understand nearly enough of this paper to write much more about it, but it contains a lot of things that I wanted to learn more about, so I’m looking forward to reading this in full at a later date. (As a bonus, this paper also finally explains just what on earth ‘classical shadows’ are, something else often talked about in the group where I work, but I’ll leave the explanation of that for another day…!)
Finite-depth scaling of infinite quantum circuits for quantum critical points, by Bernhard Jobst, Adam Smith, and Frank Pollmann: Matrix product states have become one of the main numerical tools for the study of quantum systems in one dimension, due to the way that they can efficiently encode the state of a quantum system provided that its entanglement is sufficiently low. One place where this fails is at quantum critical points, where the entanglement structure is very different to other points in the phase diagram, and here techniques exist based on an idea known as finite entanglement scaling. In the current age where quantum computers are beginning to become useful, it’s important to start asking what they’re good for. One interesting application is that a procedure known as a finite-depth quantum circuit can be used to get a quantum computer to reproduce the ground state of a given Hamiltonian, and it turns out that the resulting state can be understood as a particular case of a matrix product state. The idea is that by repeatedly applying local operations (gates) in groups known as layers, any given quantum state can be prepared by the circuit. Crucially, the output state of a quantum circuit is able to capture more entanglement that a conventional matrix product state with the same number of parameters, and so this makes quantum circuits a particularly interesting tool for future study. This work goes into detail about how information relating to quantum critical points can be extracted from finite-depth quantum circuits, and even includes benchmarks from some of IBM’s real quantum computers, albeit with very noisy data. This is an interesting work - I can’t say anything in here was a dramatic surprise, but it’s a nicely put together story that quite clearly explains every step of the process and cleared up a few confusions I had about quantum circuits, and I found it a very enjoyable paper to read.
Spectral Form Factor of a Quantum Spin Glass, by Michael Winer, Richard Barney, Christopher L. Baldwin, Victor Galitski, and Brian Swingle: Spin glasses are highly complex phases magnetic phases of matter characterised by an extremely slow relaxation to thermal equilibrium. Loosely speaking, the combination of disorder and magnetic frustation leads to a large number of possible states which are similar in energy (‘metastable states’), but separated by large energy barriers, making it difficult for the system to explore its full phase space except over extremely long time scales. This paper considers the spectral form factor of a spin glass, a quantity often studied in the context of many-body localisation in order to determine whether a system thermalises or not. As spin glasses exhibit unusually slow thermalisation, they’re a very interesting system for such a study. The authors find that spin glasses don’t exhibit chaotic statistics (to be expected from a system which equilibrates), nor do they exhibit Poisson statistics (to be expected in a fully localized system). Instead, the spin glass model they consider exhibits intermediate behaviour consistent with the idea that each metastable state is internally chaotic, but that the overall behaviour is determined by a sum over these independent metastable states, leading to a final spectral form factor that is neither chaotic nor localised, but somewhere inbetween. Having also worked on the same model of a quantum spin glass (but in my case I looked at the non-equilibrium dynamics), I found this work very impressive and the result is extremely interesting. I expect to see future work building on this, as this is too good not to follow up on!
Localization of Pairs in One-Dimensional Quasicrystals with Power-Law Hopping, by G. A. Domínguez-Castro, and R. Paredes: Often when studying localised systems, we study the behaviour of large numbers of particles, but this leads to huge computational complexity and can limit the types of simulations we can perform. In this work, the authors study pair localisation, i.e. they focus on describing the properties of just two particles moving in a disordered potential. The setting is particularly interesting - it’s a quasiperiodic system (intermediate between random and ordered), with long-range hopping (the particles are able to instantaneously make big jumps), and the authors consider both attractive and repulsive interactions. The authors find that, in contrast to models with only short-range hopping, the localisation properties depend crucially on the sign of the interactions as well as their strength. This is a nice example of how by reducing the complexity of the problem, it’s possible to make a comprehensive and insightful study of a very interesting model, when the full many-body system is much more challenging to study and can lead to results which are much more difficult to interpret.