Scientific Series

We investigate the usefulness of ground states of quantum spin chains with symmetry-protected topological order (SPTO) for measurement-based quantum computation. We show that, in spatial dimension one, if an SPTO phase supports quantum wire, then, subject to an additional symmetry condition that is satisfied in all cases so far investigated, it can also be used for quantum computation. Joint work with Dongsheng Wang, Abhishodh Prakash, Tzu-Chieh Wei and David Stephen; See arXiv:1609.07549v1

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.

Kontsevich and Soibelman defined Donaldson-Thomas invariants of a 3d Calabi-Yau category with a stability condition. Any cluster variety gives rise to a family of such categories. Their DT invariants are encapsulated in single formal automorphism of the cluster variety, called the DT-transformation. An oriented surface S with punctures, and a finite number of special points on the boundary give rise to a moduli space, closely related to the moduli space of PGL(m)-local systems on S, which carries a canonical cluster Poisson variety structure. We determine the DT-transformation of this space. This is a joint work with Alexander Goncharov.

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.

Quantum non-demolition measurements performed using qubit-based artificial atoms may enable the next generation of higher mass dark matter axion search experiments.  These QND measurements can precisely determine the amplitude of the photon wave sourced by the dark matter axions while placing the back reaction noise into the phase quadrature. By evading the standard quantum limit of phase-preserving amplifiers, the QND photon can potentially reduce readout noise by orders of magnitude.  Combined with the radio frequency quantum buses to extract the signals, the next generation axion dark matter detector may closely resemble or actually be a multi-qubit quantum computer.

The Lambda Cold Dark Matter framework successfully accounts for observational constraints on large (> 1 Mpc) scales, from the clustering of galaxies to the angular dependence of the Cosmic Microwave Background to the structure and matter content of galaxy clusters. On the scale of individual galaxies and, in particular, of dwarf systems much fainter than the Milky Way, a number of apparent conflicts with LCDM expectations have been reported. These have prompted the consideration of a number of radical modifications to LCDM, such as the possibility that dark matter might be "self-interacting", or that it might not be “cold”. I will review the status of these alleged problems and will report on recent work that reevaluates the observational evidence and reexamines the role of systematic uncertainties in the comparison between observation and model predictions. In particular, I will propose a possible resolution to the “cusp vs core” problem that requires no cores; an explanation for the mass discrepancy-acceleration relation that requires no changes to LCDM halos; and a plausible tidal origin for the enigmatic population of galaxies inhabiting “extremely cold” dark matter halos, such as the recently discovered Crater 2 satellite.

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).

A fundamental assumption of quantum statistical mechanics is that closed isolated systems always thermalize under their own dynamics. Progress on the topic of many-body localization has challenged this vital assumption, describing a phase where thermalization, and with it, equilibrium thermodynamics, breaks down.

In this talk, I will describe how we can realize such a phase of matter with ultracold fermions in both driven and undriven optical lattices, with a focus on the relevance of realistic experimental platforms. Furthermore, I will describe new results on the observation of a regime exhibiting extremely slow scrambling, even for "infinite-temperature states" in one and two dimensions. Our results demonstrate how controlled quantum simulators can explore fundamental questions about quantum statistical mechanics in genuinely novel regimes, often not accessible to state-of-the-art classical computations.

A permanent non-zero electric dipole moment of the free neutron (nEDM) violates CP-symmetry. The search for an nEDM contributes to understanding the Baryon asymmetry,
as well as it has a high discovery potential for Beyond Standard Model physics. The tool of choice to investigate the nEDM are ultracold neutrons (UCN), since they have such low energies that they can be stored in traps and allow observation times of hundreds of seconds.
The distinct feature of TRIUMFs UCN facility is the combination of a neutron spallation source with a superfluid helium UCN converter - unique among all existing and planned UCN sources worldwide. The goal of the UCN project at TRIUMF is to provide a density of several hundreds of UCN per cubic cm to experiments at up to two ports, whereas one will be dedicated to determine the nEDM to the 10-27 e·cm level of precision.
This presentation shall update the audience on the current status of the new UCN facility at TRIUMF. Additionally, a brief status update on the work of the CREMA collaboration (Charge Radius Experiments with Muonic Atoms) shall be given. Recent experiments performing laser spectroscopy on light muonic atoms shed new light on the Proton Radius Puzzle.

The first phase of stellar evolution in the history of the Universe may be Dark Stars (DS), powered by dark matter heating rather than by nuclear fusion. Weakly Interacting Massive Particles, which may be their own antipartners, collect inside the first stars and annihilate to produce a heat source that can power the stars. A new stellar phase results, a Dark Star, powered by dark matter annihilation as long as there is dark matter fuel, with lifetimes from millions to billions of years. Dark stars are very bright diffuse puffy objects during the DS phase, and grow to be very massive. In fact, we have found they can to grow to 10^5-10^7 solar masses with luminosities 10^9-10^11 solar luminosities. Such objects will be observable with James Webb Space Telescope (the sequel to HST). Once the dark matter fuel is exhausted, the DS becomes a heavy main sequence star; these stars eventually collapse to form massive black holes that may provide seeds for supermassive black holes observed at early times as well as in galaxies today.