Colloquium

Stacking two graphene layers twisted by the ‘magic angle’ 1.1º generates flat energy bands, which in turn catalyzes various strongly correlated phenomena depending on filling and sample details. While this system is most famous for the superconducting and insulating states observed at fractional fillings, I argue that charge neutrality presents an interesting interplay of disorder and interactions.

In scanning tunnelling microscopy (STM), the most striking signature of interactions occurs close to charge neutrality, where the splitting between the flat bands increases dramatically. In analogy with quantum Hall ferromagnetism, I show that this effect may be qualitatively understood as the result of an exchange energy gain. A low-energy manifold of gapped, symmetry-breaking states is identified, one of which possesses quantum valley Hall order. Transport measurements yield ostensibly conflicting information at charge neutrality: while some samples reveal semimetallicity (as expected when correlations are weak), yet others exhibit robust insulation. I reconcile these observations and those of STM by arguing that strong interactions supplemented by weak, smooth disorder stabilize a network of locally gapped quantum valley Hall domains with spatially varying Chern numbers determined by the disorder landscape—--even when an entirely different order is favored in the clean limit. I conclude with a discussion of experimental tests of this proposal via local probes and transport.

The average entanglement entropy of subsystems of random pure states is (nearly) maximal. In this talk, we discuss the average entanglement entropy of subsystems of highly excited eigenstates of integrable and nonintegrable many-body lattice Hamiltonians. For translationally invariant quadratic models (or spin models mappable to them) we prove that, when the subsystem size is not a vanishing fraction of the entire system, the average eigenstate entanglement entropy exhibits a leading volume-law term that is different from that of random pure states. We argue that such a leading term is likely universal for translationally invariant (noninteracting and interacting) integrable models. For random pure states with a fixed particle number (random canonical states) away from half filling and normally distributed real coefficients, we prove that the deviation from the maximal value grows with the square root of the system's volume when the size of the subsystem is one half of that of the system. We then show that the average entanglement entropy of highly excited eigenstates of a particle number conserving quantum chaotic model is the same as that of random canonical states.

A scientific understanding of modern deep learning is still in its early stages. As a first step towards understanding the learning dynamics of neural networks, one can simplify the problem by studying limits that might have theoretical tractability and practical relevance. I’ll begin with a brief survey of our earlier body of work that has investigated the infinite width limit of deep networks, a topic of active study recently. With these results in hand, it nonetheless appears there is still a gap towards theoretically describing neural networks at finite width. I’ll argue that the choice of learning rate is one crucial factor in dynamics away from the infinite width limit and naturally classifies deep networks into two classes separated by a sharp transition. This is elucidated in a class of solvable simple models we present, which give quantitative predictions for the two classes. Quite remarkably, we test these predictions empirically in practical settings and find excellent agreement. 

Yasaman Bahri is a research scientist on the Google Brain team. Her current research program is to build a scientific understanding of deep learning using a combination of theoretical analysis and empirical investigation. Prior to Google, she was at the University of California, Berkeley, where she received her Ph.D. in physics in 2017, specializing in theoretical quantum condensed matter.

Beginning with the landmark gravitational wave detections by LIGO/Virgo, we have been gaining an unprecedented view of the dynamics of strongly curved spacetime originally predicted by Einstein. Enabling and motivated by these observations, there has been rapid development in the theoretical and computational tools we use to understand and interpret the nature of gravity and matter in this regime. This is essential to fulfilling the promise of gravitational wave astronomy to not only be a new window on the astrophysics of black hole and neutron star mergers, but also to be a unique probe of fundamental physics. I will illustrate this, highlighting the example of how black holes can be used to search for new particles. The same theoretical tools also allow us to push Einstein's theory to the extreme in search of the limits of its predictability, for example testing cosmic censorship, the idea that the breakdown in Einstein's equations associated with unhalted collapse is always hidden behind a black hole horizon. I will describe some recent work resolving a long-standing putative counterexample to this conjecture.

While the concept of topology is often introduced by contrasting oranges with bagels, the idea of topologically distinct quantum phases of matter is far more abstract. In this talk, we will focus on a more tangible form of topology that also arises in quantum condensed matter system: when the sites in a lattice are dragged around in a symmetric manner, what attributes of the lattice would remain unchanged? Such deformation can be viewed as the lattice analog of the familiar (mental) exercise of transforming a bagel into a coffee mug. We will first introduce the mathematical framework for identifying the topological classes of lattices, and then discuss how these invariants can constrain and inform the more abstract notion of topological phases of matter that emerge.

High resolution hydrodynamic simulations of galaxy formation are powerful tools, which can provide important information on the properties of the dark matter halo. Combined with the information obtained from the second data release of the Gaia satellite, simulations can significantly improve our understanding of the dark matter distribution in the Solar neighborhood. Determining the local dark matter velocity distribution is crucial for the correct analysis and interpretation of data from dark matter direct detection experiments. I will discuss the local dark matter distribution of Milky Way-like galaxies extracted from state-of-the-art hydrodynamic simulations, and present an analysis of direct detection data using this distribution. I will also discuss the properties of the dark matter component of the radially anisotropic stellar population recently discovered in the Gaia data, using the Auriga simulations. In particular, I will present the local dark matter density and velocity distributions of the simulated Milky Way-like galaxies with and without the anisotropic substructure, and discuss their implications for dark matter direct detection.

Last fall, a team at Google announced the first-ever demonstration of "quantum computational supremacy"---that is, a clear quantum speedup over a classical computer for some task---using a 53-qubit programmable superconducting chip called Sycamore.  In addition to engineering, Google's accomplishment built on a decade of research in quantum computing theory.  This talk will discuss questions like: what exactly was the contrived computational problem that Google solved?  How does one verify the outputs using a classical computer?  And how confident are we that the problem really is classically hard---especially in light of subsequent counterclaims by IBM?  I'll end with a proposed application for Google's experiment---namely, the generation of certified random bits, for use (for example) in proof-of-stake cryptocurrencies---that I've been developing and that Google is now working to demonstrate.

Fundamental physics (including physics beyond the Standard Model) can be tested using table-top precision measurements. The talk will describe measurements of the size of the proton, the fine-structure constant and the electric dipole moment of the electron. Two recently completed measurements will be described. For the first measurement, the n=2 Lamb shift of atomic hydrogen is measured, allowing for a new determination of the charge radius of the proton. This determination is crucial to resolving the decade-old proton radius puzzle, in which it appeared that the proton radius took on a different value when measured with muons compared to measurements using electrons. The second measurement is of the n=2 triplet P fine structure of atomic helium, and this work is part of a program to obtain a new determination of the fine-structure constant. Both of these measurements use a new measurements technique: Frequency offset separated oscillatory fields. Finally, a new major effort (EDM^3) is starting at York University to measure the electron electric dipole moment using polar molecules embedded into inert-gas solids. This measurement will test for T violation and will probe physics up to the PeV energy scale.    

Our ability to model cosmological observations has reached an awesome level, a tour de force of observational innovation, sophisticated statistical inference, and delicate numerical computation. There’s little doubt that the Standard Cosmological Model will stand the test of time. But what has it told us and what is still missing? What are the prospects for learning particle physics and condensed matter from cosmology? And what can the path we’ve taken to reach this point tell us about where it might lead?

I will start with an introduction into the framework of perturbative algebraic quantum field theory (pAQFT), which is a mathematically rigorous approach to perturbative QFT. In its original formulation, it is based on the Haag-Kastler axiomatic framework, where locality is a fundamental principle. In my talk I will discuss how it can be extended to treat also non-local observables, with potential applications to effective quantum gravity

At the heart of the quantum measurement problem lies the ambiguity about exactly when to use the unitary evolution of the quantum state and when to use the state-update in dynamics of quantum mechanical systems. In the Wigner’s friend gedankenexperiment, different observers (one of whom is observed by the other) describe one and the same interaction differently. One – the friend – uses the state-update rule and the other – Wigner – chooses unitary evolution. This can lead to paradoxical situations in which Wigner and his friend assign different probabilities to the outcomes of subsequent measurements. In my talk, I will apply the Page-Wootters mechanism (PWM) as a timeless description of the Wigner's friend-like scenario. This description assigns one timeless state to the entire experimental scenario from which it is possible to derive probabilities without the need to involve the evolution of the quantum state during – and in-between – measurements. I will consider several rules for assigning two-time conditional probabilities within the PWM. All of these reduce to standard (“textbook”) rules for non-Wigner’s friend scenarios. However, when applied to the Wigner’s friend setup, they differ. Each rule potentially resolves the probability-assignment paradox in a different way. Moreover, one rule imposes that a joint probability distribution for the measurement outcomes of Wigner and his friend is well-defined only when Wigner’s measurement does not disturb the friend’s memory, in agreement with the recent “no-go theorem for observer-independent facts

(with Veronika Baumann, Flavio Del Santo, Alexander R. H. Smith, Flaminia Giacomini, and Esteban Castro-Ruiz)

Cosmological simulations of galaxy formation have evolved significantly over the last years.
In my talk I will describe recent efforts to model the large-scale distribution
of galaxies with cosmological hydrodynamics simulations. I will focus on the
Illustris simulation, and our new simulation campaign, the IllustrisTNG
project. After demonstrating the success of these simulations in terms of
reproducing an enormous amount of observational data, I will also talk about
their limitations and directions for further improvements over the next couple
of years.