Physics

Existing proposals for topological quantum computation have encountered
difficulties in recent years in the form of several ``obstructing'' results.
These are not actually no-go theorems but they do present some serious
obstacles. A further aggravation is the fact that the known topological
error correction codes only really work well in spatial dimensions higher
than three. In this talk I will present a method for modifying a higher
dimensional topological error correction code into one that can be embedded
into two (or three) dimensions. These projected codes retain at least some
of their higher-dimensional topological properties. The resulting subsystem
codes are not discrete analogs of TQFTs and as such they evade the usual
obstruction results. Instead they obey a discrete analog of a conformal
symmetry. Nevertheless, there are real systems which have these features,
and if time permits I'll discuss some of these. Many of them exhibit
strange low temperature behaviours that might even be helpful for
establishing finite temperature fault tolerance thresholds.

This research is still very much a work in progress... As such it has
numerous loose ends and open questions for further investigation. These
constructions could also be of interest to quantum condensed matter
theorists and may even be of interest to people who like weird-and-wonderful
spin models in general.

Over the past several years, our understanding of topological electronic phases of matter has advanced dramatically.   A paradigm that has emerged is that insulating electronic states with an energy gap fall into distinct topological classes.   Interfaces between different topological phases exhibit gapless conducting states that are protected topologically and are impossible to get rid of.   In this talk we will discuss the application of this idea to the quantum Hall effect, topological insulators,  topological superconductors and the quest for Majorana fermions in condensed matter.   We will then show that similar ideas arise in a completely different class of problems.    Isostatic lattices are arrays of masses and springs that are at the verge of mechanical instability.   They play an important role in our understanding of granular matter, glasses and other 'soft' systems.  Depending on their geometry, they can exhibit zero-frequency 'floppy' modes localized on their boundaries that are insensitive to local perturbations.   The mathematical relation between this classical system and quantum electronic systems reveals an unexpected connection between theories of hard and soft matter.

Given two sets X and Y, we consider synchronous correlations in a two-party nonlocal game with inputs X and outputs Y as a notion of generalized function between these sets (akin to a quantum graph homomorphism). We examine some structures in categories of synchronous classical, quantum, and nonsignalling strategies. We also provide analogues of Bell’s inequalities for such games when Y = {0,1}.

The existence of a deconfined quantum-critical point [1] between the standard antiferromagnet
and a valence-bond solid in 2D S=1/2 quantum magnets has been controversial, in part due to
anomalous finite-size scaling behaviors observed in quantum Monte Carlo simulations interpreted by some as signs of a first-order transition. I will discuss a new finite-size scaling hypothesis in which a scaling function of two divergent length scales [the standard correlation length and a length-scale related to an emergent U(1) symmetry of the valence-bond solid] has a limiting form implying unconventional finite-size scaling behaviors, while maintaining conventional scaling in the thermodynamic limit [2]. This proposal goes beyond the standard scenario of a dangerously irrelevant perturbation as a source of the second length scale in, e.g., classical 3D clock models. Quantum Monte Carlo simulations of the J-Q model (a spin-1=2 Heisenberg model extended with certain multi-spin interactions) are in full agreement with the proposed scaling form, suggesting that deconfined quantum-criticality is an even richer phenomenon than initially imagined. Since finite temperature T plays the role of a finite imaginary-time dimension in quantum systems, the anomalous scaling behavior impacts also the scaling in the quantum-critical \fan" at T > 0. This is also observed in the J-Q model.

[1] H. Shao, W. Guo, and A. W. Sandvik, Science 352, 213 (2016).
[2] T. Senthil, A. Vishwanath, L. Balents, S. Sachdev, M. P. A. Fisher, Science 303, 1490 (2004).

An overview will be given of recently discovered connection between asymptotic symmetries in general relativity  and soft theorems in quantum field theory together with their implications for the black hole information paradox.

I will first show that a number of persistent astrophysical puzzles, including missing pulsars in the galactic center, fast radio bursts, the abundance of r-process elements, and the type Ia supernova progenitor problem, may all be an emerging signature of dark matter. I will address some theoretical implications and new astrophysical phenomena -- for example "quiet kilonovae" and "r-process donuts" -- associated with this dark matter. Then, I will describe a newly discovered effect, that dark matter crashing into neutron stars warms them to infrared temperatures detectable with the Thirty Meter, European Extremely Large, and James Webb Space telescopes.

Dark matter is all around us, however its particle physics nature is still mysterious. Searches for dark matter have largely focused on candidates with weak scale interactions to the standard model particles, the so-called WIMP paradigm. However, the parameter space of the WIMP paradigm is becoming increasingly constrained by both the LHC and direct detection experiments. Another possibility that is well motivated both theoretically and observationally is to have a dark sector connected with the visible one via a mediator whose coupling to the visible one is tiny. In this talk, based on my own work, I will discuss models in this direction and how to search for signals from the dark sector using various experiments including particle accelerators, dark matter direct detection experiments, cosmic ray experiments, and cosmic microwave background observation. 

The origin and composition of 85% of the matter in the universe is completely unknown. Among several viable options, Weakly Interacting Massive Particles (WIMPs) are motivated dark matter candidates that can be tested by different and complementary search strategies. Crucially, different searches probe WIMP couplings at different energy scales, and such a separation of scales has striking consequences in connecting different experimental probes. This motivates the development of theoretical tools to properly connect the different energy scales involved in constraining WIMP models. I will introduce these tools and I will illustrate with several examples how crucial the inclusion of these effects in WIMP searches is.

More than a billion years ago, two black holes collided. In the final second of their long life together, the black holes banged out a rhythm like mallets on a drum, creating gravitational waves – ripples in the shape of spacetime. One hundred years ago, Albert Einstein predicted the existence of such waves, though it seemed improbable – if not outright impossible – that we’d ever be able to actually detect them. They were long considered too faint for any earthbound experiment to measure. Undaunted, experimentalists were determined to measure these Lilliputian ripples, and after many decades of work and collaboration, they built LIGO – the Laser Interferometer Gravitational-Wave Observatory. This incredible sophisticated and sensitive instrument was made to listen for the beat of that distant drum. In 2015, a billion years after the two black holes collided, their waves rippled through the LIGO detectors in Louisiana and Washington. With these remarkable new observatories, we can now capture the soundtrack to accompany the silent movie of the history of our universe.