Scientific Series

Entanglement and entropy are key concepts standing at the foundations of quantum and statistical mechanics, respectively. In the last decade the study of quantum quenches revealed that these two concepts are intricately intertwined. Although the unitary time evolution ensuing from a pure initial state maintains the system globally at zero entropy, at long time after the quench local properties are captured by an appropriate statistical ensemble with non zero thermodynamic entropy, which can be interpreted as the entanglement accumulated during the dynamics. Therefore, understanding the post-quench entanglement evolution unveils how thermodynamics emerges in isolated quantum systems. An exact computation of the entanglement dynamics has been provided only for non-interacting systems, and it was believed to be unfeasible for genuinely interacting models. Conversely, here we show that the standard quasiparticle picture of the entanglement evolution, complemented with integrability-based knowledge of the asymptotic state, leads to a complete analytical understanding of the entanglement dynamics in the space-time scaling limit. Our framework requires only knowledge about the steady state, and the velocities of the low-lying excitations around it. We provide a thorough check of our result focusing on the spin-1/2 Heisenberg XXZ chain, and considering quenches from several initial states. We compare our results with numerical simulations using both tDMRG and iTEBD, finding always perfect agreement.

While originally motivated by quantum computation, quantum error correction (QEC) is currently providing valuable insights into many-body quantum physics such as topological phases of matter. Furthermore, mounting evidence originating from holography research (AdS/CFT), indicates that QEC should also be pertinent for conformal field theories. With this motivation in mind, we introduce quantum source-channel codes, which combine features of lossy-compression and approximate quantum error correction, both of which are predicted in holography. Through a recent construction for approximate recovery maps, we derive guarantees on its erasure decoding performance from calculations of an entropic quantity called conditional mutual information. As an example, we consider Gibbs states of the transverse field Ising model at criticality and provide evidence that they exhibit non-trivial protection from local erasure. This gives rise to the first concrete interpretation of a bona fide conformal field theory as a quantum error correcting code. We argue that quantum source-channel codes are of independent interest beyond holography.

What can machine learning teach us about quantum mechanics? I will begin with a brief overview of attempts to bring together the two fields, and the insights this may yield. I will then focus on one particular framework, Projective Simulation, which describes physics-based agents that are capable of learning by themselves. These agents can serve as toy models for studying a wide variety of phenomena, as I will illustrate with examples from quantum experiments and biology.

Branch point twist fields play an important role in the study of measures of entanglement such as the Rényi entropies and the Negativity. In 1+1 dimensions such measures can be written in terms of multi-point functions of branch point twist fields. For 1+1-dimensional integrable quantum field theories and also in conformal field theory much is known about how to compute correlation functions and, with the help of the twist field, this knowledge can be exploited in order to gain new insights into the properties of various entanglement measures. In this talk I will review some of our main results in this context.

I will then go on to introduce a new (related) class of fields we have recently named conical twist fields. These are fields whose two-point functions have (surprisingly) been found to describe gluon amplitudes in the strong coupling limit of super Yang-Mills theories and therefore have featured in a completely different context from that of entanglement measures. Interestingly, at critical points, branch point and conical twist fields have the same conformal dimension and beyond criticality they also have very similar form factors, however they are different in many other respects.  In my talk I will discuss and justify some of their similarities and differences.

A state is called a Markov state if it fulfil the important condition of saturating the Strong Subadditivity inequality. I will show how the vacuum state of any relativistic QFT is a Markov state when reduced to certain geometric regions of spacetime. A characterisation of this regions will be presented as well as two independent proofs of the Markov condition in QFT. 

For the CFT vacuum, the Markov property is the key ingredient to prove the a-theorem (irreversibility of the RG flow in QFT in d=4 spacetime dimensions) using vacuum entanglement entropy. This extends the entropic proofs of the c and F theorems in dimensions d=2 and d=3 and gives a unified picture of all the known irreversibility theorems in QFT. 

I will also comment on the relation of this Markov property with the unitarity bound and other information theory inequalities.

Many of the multi-planet systems discovered around other stars are maximally packed. This implies that simulations with masses or orbital parameters too far from the actual values will destabilize on short timescales; thus, long-term dynamics allows one to constrain the orbital architectures of many closely packed multi-planet systems. I will present a recent such application in the TRAPPIST-1 system, with 7 Earth-sized planets in the longest resonant chain discovered to date. In this case the complicated resonant phase space structure allows for strong constraints. A central challenge in such studies is the large computational cost of N-body simulations, which preclude a full survey of the high-dimensional parameter space of orbital architectures allowed by observations. I will discuss our recent successes in training machine learning models capable of predicting orbital stability a million times faster than N-body simulations, and the discovery space that this opens up for exoplanet characterization and planet formation studies.

Dataset augmentation, the practice of applying a wide array of domain-specific transformations to synthetically expand a training set, is a standard tool in supervised learning. While effective in tasks such as visual recognition, the set of transformations must be carefully designed, implemented, and tested for every new domain, limiting its re-use and generality. In this talk, I will describe recent methods that  transform data not in input space, but in a feature space found by unsupervised learning. We start with data points mapped to a learned feature space and apply simple transformations such as adding noise, interpolating, or extrapolating between them. Working in the space of context vectors generated by sequence-to-sequence recurrent neural networks, this simple and domain-agnostic technique is demonstrated to be effective for both static and sequential data. 

Bio: Graham Taylor is an Associate Professor at the University of Guelph where he leads the Machine Learning Research Group. He is a member of the Vector Insitute for Artificial Intelligence and is an Azrieli Global Scholar with the Canadian Institute for Advanced Research. He received his PhD in Computer Science from the University of Toronto in 2009, where he was advised by Geoffrey Hinton and Sam Roweis. He spent two years as a postdoc at the Courant Institute of Mathematical Sciences, New York University working with Chris Bregler, Rob Fergus, and Yann LeCun. 

Dr. Taylor's research focuses on statistical machine learning, with an emphasis on deep learning and sequential data. Much of his work has focused on "seeing people" in images and video, for example, activity and gesture recognition, pose estimation, emotion recognition, and biometrics.

Calculating the path integral over all causal sets will take a lot of computing power, and requires a way to suppress non-manifold like causal sets. To work towards these goals we can start by taking the path integral over a restricted class of causal sets, the 2d orders. Using these have found a phase transition and been able to study the Hartle-Hawking wave function in causal sets. In this talk I will present these recent results (arXiv:1410.8775 and arXiv:1706.06432), and some preliminary data exploring how the behavior of the 2d orders is influenced by coupling them to an Ising model.

After a small review on divergent series and Borel resummation I will discuss a geometric approach based on Picard-Lefschetz theory to study the interplay between perturbative and non-perturbative effects in the QM path integral.

Such approach can be used to characterize when the perturbative series gives the full answer and when the inclusion of non-trivial saddles--instantons--is mandatory. I will then show how a simple deformation of the original perturbation theory allows to recover the full non perturbative answer from the perturbative coefficients alone, without the need of including instanton corrections. I will illustrate this technique in examples which are known to contain non-perturbative effects, such as the (supersymmetric) double-well potential, the pure anharmonic oscillator, and the perturbative expansion around a false vacuum.

The hydrodynamic approximation is an extremely powerful tool to describe the behavior of many-body systems such as gases. At the Euler scale (that is, when variations of densities and currents occur only on large space-time scales), the approximation is based on the idea of local thermodynamic equilibrium: locally, within fluid cells, the system is in a Galilean or relativistic boost of a Gibbs equilibrium state. This is expected to arise in conventional gases thanks to ergodicity and Gibbs thermalization, which in the quantum case is embodied by the eigenstate thermalization hypothesis. However, integrable systems are well known not to thermalize in the standard fashion. The presence of infinitely-many conservation laws preclude Gibbs thermalization, and instead generalized Gibbs ensembles emerge. In this talk I will introduce the associated theory of generalized hydrodynamics (GHD), which applies the hydrodynamic ideas to systems with infinitely-many conservation laws. It describes the dynamics from inhomogeneous states and in inhomogeneous force fields, and is valid both for quantum systems such as experimentally realized one-dimensional interacting Bose gases and quantum Heisenberg chains, and classical ones such as soliton gases and classical field theory. I will give an overview of what GHD is, how its main equations are derived, its relation to quantum and classical integrable systems, and some geometry that lies at its core. I will then explain how it reproduces the effects seen in the famous quantum Newton cradle experiment, and how it leads to exact results in transport problems such as Drude weights and non-equilibrium currents.

This is based on various collaborations with Alvise Bastianello, Olalla Castro Alvaredo, Jean-Sébastien Caux, Jérôme Dubail, Robert Konik, Herbert Spohn, Gerard Watts and my student Takato Yoshimura, and strongly inspired by previous collaborations with Denis Bernard, M. Joe Bhaseen, Andrew Lucas and Koenraad Schalm.

The study of super-Eddington accretion is essential to our understanding of the growth of super-massive black holes in the early universe, the accretion of tidally disrupted stars, and the nature of ultraluminous X-ray sources.  Unfortunately, this mode of accretion is particularly difficult to model because of the multidimensionality of the flow, the importance magnetohydrodynamic turbulence, and the dominant dynamical role played by radiation forces.  However, recent increases in computing power and advances in algorithms are facilitating major improvements in our ability to model radiation in numerical simulations of astrophysical plasmas.  I will briefly describe our new radiation transfer modules and discuss our efforts to model super-Eddington accretion flows around stellar mass and supermassive black holes.  I will focus on applications to ultraluminous X-ray sources, which must be radiating well above their Eddington luminosity unless they harbour intermediate mass black holes. I will argue that most of these sources can be (and likely are) "normal" ~10 solar mass black holes accreting and radiating with luminosities well above their Eddington "limit”.