Scientific Series

It has long been argued that combining the uncertainty principle with gravity will lead to an effective minimum length at the Planck scale. A particular challenge is to model the presence of a smallest length scale in a manner which respects continuous spacetime symmetries. One path for deriving low-energy descriptions of an invariant minimum length in quantum field theory is based on generalized uncertainty principles. Here I will consider the question how this approach enables one to retain Euclidean or even Lorentzian symmetries. The Euclidean case yields a ultraviolet cutoff in the form of a bandlimit, and this then allows one to apply the powerful Shannon sampling theorem of classical information theory which establishes the equivalence between continuous and discrete representations of information. As a consequence, one obtains discrete representations of fields which are more subtle than a simple discretization of space, and are in fact equivalent to a continuum representation. Quantum fields in this model exhibit a finite density of information and a corresponding regularization of the entanglement of the vacuum, as I will demonstrate in detail. We then examine the Lorentzian symmetry generalization. This case leads to a Lorentz-invariant analogue of bandlimitation, and we discuss the nature of the corresponding sampling theory.

In this talk I will present a construction of relative Bridgeland stability conditions that appeared in my work on stability of topological Fukaya categories of surfaces. This construction gives a local-to-global tool for constructing stability conditions. I will explain what technical features of such Fukaya categories render this construction useful in their context, and time allowing discuss the challenges involved in applying these ideas to other contexts such as Bridgeland-Smith type stability conditions and topological Fukaya categories with coefficients.

Simulations that numerically solve Einstein's equations are the only means to accurately predict the outcome of the merger of two black holes. The most important outputs from these simulations are the gravitational waveforms, and the mass and spin of the final black hole formed after the merger. The waveforms are used in extracting astrophysical information from detections, while the final mass and spin are used in testing general relativity. Unfortunately, these simulations are too expensive for direct use in data analysis; each simulation can take a month on a supercomputer. Surrogate modeling is a data-driven approach to modeling, that uses machine learning like techniques to interpolate between hundreds of existing simulations. In this talk, I will discuss some recent developments in surrogate modeling, including a new 7-dimensional model that fully captures the effects of precession; the wobbling of the orbit caused when the black holes’ spin axes aren’t perpendicular to the plane of the orbit. This model reproduces the waveform as well as the final black hole's mass and spin as accurately as the simulations themselves, while taking only a fraction of a second to evaluate on a laptop.

Connections between 2D gapped quantum phases and the anyon fusion theory have been proven in various ways under different settings. In this work, we introduce a new framework connecting them by only assuming a conjectured form of entanglement area law for 2D gapped systems. We show that one can systematically define topological charges and fusion rules from the area law alone, in a well-defined way. We then derive the fusion rules of charges satisfy all the axioms required in the algebraic theory of anyons. Moreover, even though we make no assumption about the exact value of the constant sub-leading term of the entanglement entropy, this term is shown to be equal to the logarithm of the total quantum dimension of the anyon theory we defined. 

Many complex systems have a generative, or linguistic, aspect: life is written in the language of DNA; protein structure is written in a language of amino acids, and human endeavour is often written in text. Are there universal aspects of the relationship between sequence and structure? I am trying to answer this question using models of random languages. Recently I proposed a model of random context-free languages [1] and showed using simulations that the model has a transition from an unintelligent phase to an ordered phase. In the former, produced sequences look like noise, while in the latter they have a nontrivial Shannon entropy; thus the transition corresponds to the emergence of information-carrying in the language. 

In this talk I will explain the basics of natural language syntax, without assuming any prior knowledge of linguistics. I will present the results from the model above, and explain how the model is related to complex matrix models with disorder [2].

[1] https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.122.128301

[2] https://arxiv.org/abs/1902.07516

QFTs in 2+1 dimensions are powerful systems to understand the emergence of mass-gap and particle spectrum in QCD-like theories that describe our 3+1 dimensional world. Recently, these 2+1 dimensional systems have attracted even more attention due to conjectured dualities between seemingly very different theories and due to their applications to condensed matter systems. In this talk, I will describe our numerical investigations of the infrared behaviors of 2+1 dimensional U(1) and SU(N) gauge theories coupled to many favors of massless fermions using lattice regularization. I will also explain how lattice formulation is a potential tool to study and check particle-vortex dualities.

Can a relativistic quantum field theory be consistently described as a theory of localizable particles? There are many well-known obstructions to such a description. Here, we trace exactly how such obstructions arise in the regime between nonrelativistic quantum mechanics and relativistic quantum field theory. Perhaps unexpectedly, we find that in the nonrelativistic limit of QFT, there are persisting issues with the localizability of particle states. Related via the Reeh-Schlieder theorem, we also show that the fate of ground state entanglement and the Unruh effect is nontrivial in the nonrelativistic limit.

The influx of new and high-quality cosmological data from upcoming cosmic microwave background (CMB) and large-scale structure surveys will provide unique and exciting opportunities to study the fundamental constituents of the Universe in the upcoming few years. In particular, measurements of second-order effects in the CMB will become observationally significant for the fist time as surveys will achieve the necessary precision. Such second-order effects include weak gravitational lensing by large-scale structure; the integrated Sachs-Wolfe and Rees-Sciama effects, which describe the redshift effect on CMB photons due to evolving gravitational potentials along the line of sight; and the Sunyaev-Zel'dovich effect where CMB photons Compton scatter with free electrons in galaxy clusters and the intergalactic medium. In parallel, surveys of the 21cm hydrogen line will achieve sufficient accuracy for cosmological inference. In this talk I will describe how these new cosmological probes provide opportunities to study old fundamental problems. I will focus on two new probes: the moving lens effect on the CMB (Hotinli 2019, PRL) and the velocity acoustic oscillations (`so-called' VAOs) in the 21cm hydrogen. I will describe how these observables can be utilised to constrain a class of early Universe models.

Defining entanglement in a continuum field theory is a subtle challenge, because the Hilbert space does not naively factorize into local products.   For gauge theories, the problem arises from the gauss law constraint, and it can be resolved by an extension of the Hilbert space which introduces edge modes at the entangling surface.  Recently we showed how this extension  fits inside the frame work of 2D extended topological field theory.  In this talk we attempt a generalization to 2D CFTs in which factorization is determined by the fusion rules.  Time permitting we will speculate on applications, e.g to continuum constructions of tensor networks and to entanglement in string theory 

Docker provides "containerization" for software -- a way to package up a piece of software and all its dependencies, so that it can run the same way on different computers.  It is a promising technology for scientists, both for reproducibility, ease of collaboration, and for running software on different computers (like your laptop and different clusters).  I will go through the why and how of using Docker.  For supercomputers (such as our Symmetry machine), Docker isn't allowed due to security issues, but the Singularity program allows users to run Docker containers, so I'll show you how to run your Docker container on Symmetry using Singularity.

milliQan is a proposed search for milli-charged particles produced at the LHC with expected sensitivity to charges of between 0.1e and 0.001e for masses in 0.1 - 100 GeV range. The proposed detector is an array of 4 stacks of 60 cm long plastic scintillator arrays read out by PMTs. It will be installed in an existing tunnel 33 m from the CMS interaction point at the LHC, with 17 m of rock shielding to suppress beam backgrounds. In the fall of 2017 a 1% scale “demonstrator” of the proposed detector was installed at the planned site in order to study the feasibility of the experiment, focusing on understanding various background sources such as radioactivity of materials, PMT dark current, cosmic rays, and beam induced backgrounds. In this talk I will discuss the general concept of the experiment, the results from the demonstrator, and the plan for the future.

A tremendous amount of recent attention has focused on characterizing the dynamical properties of periodically driven many-body systems. Here, we use a novel numerical tool termed ‘density matrix truncation’ (DMT) to investigate the long-time dynamics of large-scale Floquet systems. By implementing a spatially inhomogeneous drive to a 1D quantum chain, we demonstrate that an interplay between Floquet heating and diffusive transport is crucial to understanding the system’s dynamics. We find that DMT accurately captures two essential pieces of Floquet physics, namely prethermalization and late-time heating to infinite temperature. Moreover, we show that these two aspects are driven by different microscopic mechanisms.