Talks

In the summer of 2015, the speaker led a team at Microsoft Research, comprised primarily of research interns from seven universities, to demonstrate a social, ambulatory, Mixed Reality system for the first time.  Each intern developed a preliminary, domain-specific exploration of how such a system could be used.  One of the interns, Andrzej Banburski of the Perimeter Institute, demonstrated an interface to Mathematica.  The very concept and terminology of Virtual Reality had been first articulated by the speaker almost four decades earlier precisely in the hopes of experiencing this type of interface.  Mathematical expressions floating in the air is not just more vivid that writing them on a blackboard; a different workflow and mental framework becomes possible.  For instance, functions appear as lenses that can be compounded as they are lined up.  One can peer through a stack of such lenses at different data or starting conditions.  Instead of erasing and replacing portions of expressions on a blackboard, a stack of lenses can fork and merge, so that a range of variations can be explored at once as aspects of a sculptural form.   The purpose is not just to make math more accessible to those who might find this interface more inviting, but to free math from pre-computational, notation-bound conventions.  The speaker will argue that this type of interface, while still only barely explored, could eventually have a significant impact both on computer science and other disciplines, including theoretical physics. 

K-theoretical/Cohomological Hall algebras, associated with the stack of zero-dimensional sheaves on $\mathbb{C}^2$, play a prominent role in the proof, given by Schiffmann and Vasserot, of the AGT conjecture for

(pure) gauge theories on $\mathbb{C}^2$. In the present talk I will describe K-theoretic/Cohomological Hall algebras associated with stacks of torsion sheaves on A-type ALE spaces and their representations; the study of these algebras will provide eventually an approach to prove the AGT conjecture for (pure) gauge theories on A-type ALE spaces. (Work in progress with Olivier Schiffmann.)

This is the first of two talks on recent advances in our understanding of hydrodynamics as a generic theory of near-thermal dynamics of density matrices. In this talk I will focus on the structure of the hydrodynamic gradient expansion subject to the Second Law of thermodynamics. I will present an eightfold classification scheme and an explicit solution at all orders in derivatives of hydrodynamic transport consistent with the Second Law. I will also mention some connections with gravity and argue that the classification hints towards the existence of a gauge theory whose symmetry current is the entropy current. (The topic of my second, independently accessible, talk on Nov 20 will be a detailed field theoretic proposal for how these and other interesting features emerge from microscopic Schwinger-Keldysh formalism.)

Scalable anyonic topological quantum computation requires the error-correction of non-abelian anyon systems. In contrast to abelian topological codes such as the toric code, the design, modelling, and simulation of error-correction protocols for non-abelian anyon codes is still in its infancy. Using a phenomenological noise model, we adapt abelian topological decoding protocols to the non-abelian setting and simulate their behaviour. We also show how to simulate error-correction in universal anyon models by exploiting the special structure of typical noise patterns.

A quantum entanglement is a special kind of correlation; it may yield a strong correlation that is not possible in a classical ensemble, or hide the correlation from all local observables. Especially important is the entanglement that arises from local interactions for its implications in many-body physics and future’s quantum technologies.
I will review a few characteristics of entangled qubits in connection to fault-tolerant quantum information processing, and present a class of long-range entangled many-body states that are ground states of gapped local Hamiltonians on lattices. The class is qualitatively unconventional in many ways, and substantially boosts the richness of many-body entanglement. Implications in mechanisms of localization, renormalization group flow, quantum information storage, and topological order will be discussed.

The talk first offers a brief assessment of the realist and nonrealist understanding of quantum theory, in relation to the role of probability and statistics there from the perspective of quantum information theory, in part in view of several recent developments in quantum information theory in the work of M. G. D’Ariano and L. Hardy, among others. It then argues that what defines quantum theory, both quantum mechanics and quantum field theory, most essentially, including as concerns realism or the lack thereof and the probability and statistics, is a new (vs. classical physics or relativity) role of technology in quantum physics. This role was first considered by Bohr in his analysis of the fundamental role of measuring instruments in the constitution of quantum phenomena, which, he argued, is responsible for the difficulties of providing a realist description of quantum objects and their behavior, and, correlatively, for the irreducibly probabilistic or statistical nature of all quantum predictions. In this paper, I mean “technology” in a broader sense, akin to what the ancient Greeks called “tekhne” (“technique”). It refers the means by which we create new mental and material constructions, such as mathematical, scientific, or philosophical theories or works of art and architecture, or machines, and through which we interact with the world. I shall consider three forms of technology—mathematical, experimental, and digital. The relationships among them were crucial to the discovery of the Higgs boson, and, I argue, are likely to remain equally crucial, indeed unavoidable, in the future of physics, especially quantum physics.

While entanglement entropy of ground states usually follows the area law, violations do exist, and it is important to understand their origin. In 1D they are found to be associated with quantum criticality. Until recently the only established examples of such violation in higher dimensions are free fermion ground states with Fermi surfaces, where it is found that the area law is enhanced by a logarithmic factor.  In Ref. [1], we use multi-dimensional bosonization to provide a simple derivation of this result, and show that the logarithimic factor has a 1D origin. More importantly the bosonization technique allows us to take into account the Fermi liquid interactions, and obtain the leading scaling behavior of the entanglement entropy of Fermi liquids. The central result of our work is that Fermi liquid interactions do not alter the leading scaling behavior of the entanglement entropy, and the logarithmic enhancement of area law is a robust property of the Fermi liquid phase. In sharp contrast to the fermioic systems with Fermi surfaces, quantum critical (or gapless) bosonic systems do not violate the area law above 1D (except for the case discussed below). The fundamental difference lies in the fact that gapless excitations live near a single point (usually origin of momentum space) in such bosonic systems, while they live around an (extended) Fermi surface in Fermi liquids. In Ref. [2], we studied entanglement properties of some specific examples of the so called Bose metal states, in which bosons neither condense (and become a superfluid) nor localize (and

insulate) at T=0. The system supports gapless excitations around ``Bose surfaces", instead of isolated points in momentum space. We showed that similar to free Fermi gas and Fermi liquids, these states violate the entanglement area law in a logarithmic fashion. Compared to ground states, much less is known concretely about entanglement in

(highly) excited states. Going back to free fermion systems, in [3] we show that there exists a duality relation between ground and excited states, and the area law obeyed by ground state turns into a volume law for excited states, something that is widely expected but very hard to prove. Most importantly, we find in appropriate limits the reduced density matrix of a subsystem takes the form of thermal density matrix, providing an explicit example of the eigenstate thermalization hypothesis. Our work [3] explicitly demonstrates how statistical physics emerges from entanglement in a single eigenstate.

[1] Entanglement Entropy of Fermi Liquids via Multi-dimensional Bosonization, Wenxin Ding, Alexander Seidel, Kun Yang, Phys. Rev. X 2,

011012 (2012).

[2] Violation of Entanglement-Area Law in Bosonic Systems with Bose

Surfaces: Possible Application to Bose Metals, Hsin-Hua Lai, Kun Yang, N.

E. Bonesteel, Phys. Rev. Lett. 111, 210402 (2013).

[3] Entanglement entropy scaling laws and eigenstate thermalization in free fermion systems, Hsin-Hua Lai, Kun Yang, Phys. Rev. B 91,081110 (2015)