Condensed Matter

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.

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.

Frustrated magnets provide a fertile ground for discovering exotic states of matter, such as those with topologically non-trivial properties. Motivated by several near-ideal material realizations, we focus on aspects of the two-dimensional kagome antiferromagnet. I present two of our works in this area both involving the spin-1/2 XXZ antiferromagnetic Heisenberg model. First, guided by a previous field theoretical study, we explore the XY limit ($J_z=0$) for the case of 2/3 magnetization (i.e. 1/6 filling of hard-core bosons) and perform exact numerical computations to search for a "chiral spin liquid phase". We provide evidence for this phase by analyzing the energetics, determining minimally entangled states and the associated modular matrices, and evaluating the many-body Chern number [1]. The second part of the talk follows from an unexpected outcome of the first work, which realized the existence of an exactly solvable point for the ratio of Ising to transverse coupling $J_z/J=-1/2$. This point in the phase diagram has "three coloring" states as its exact ground states, exists for all magnetizations (fillings) and is found to be the source or "mother" of the observed phases of the kagome antiferromagnet. Using this viewpoint, I revisit certain aspects of the highly contentious Heisenberg case (in zero field) and suggest that it is possibly part of a line of critical points.

[1] K. Kumar, H. J. Changlani, B. K. Clark, E. Fradkin, Phys. Rev. B 94, 134410 (2016)
[2] H. J. Changlani, D. Kochkov, K. Kumar, B. K. Clark, E. Fradkin, under review.

Many model quantum spin systems have been proposed to realize critical points or phases described by 2+1 dimensional conformal gauge theories. On a torus of size L and modular parameter τ, the energy levels of such gauge theories equal (1/L) times universal functions of τ. We compute the universal spectrum of QED3, a U(1) gauge theory with Nf two-component massless Dirac fermions, in the large-Nf limit. We also allow for a Chern-Simons term at level k, and show how the topological k-fold ground state degeneracy in the absence of fermions transforms into the universal spectrum in the presence of fermions; these computations are performed at fixed Nf/k in the large-Nf limit.