Scientific Series

I will give an introduction to the geometric aspects of Lie algebroids and show how they give the correct framework to discuss gauge theories. The analysis is solely based on geometry, and thus applies to every gauge theory, independently of their specific features and dynamics. By thoroughly re-formulating the physical content of gauge theories on Atiyah Lie algebroids, we will show that the BRST construction is part of the formalism, indicating a fascinating interplay between classical geometry and quantum physics. Time permitting, we will show how our setup encompasses gravitational theories too, once the frame bundle and solder form are added to the picture.

It is known that constraints imposed by causality and unitarity of four-particle scattering amplitudes lead to non-trivial requirements on the low energy effective field theory coefficients. We introduce families of linear and nonlinear inequalities resulting from a systematic study of positive geometry structure hidden in those constraints.

I will present a new  mechanism for superconductivity from strong electron-electron repulsion in multi-band systems. When the kinetic energy is small, the dynamics of nearby electrons on the lattice is strongly correlated. I will introduce a controlled expansion in the kinetic term to demonstrate pairing induced by correlated tunneling process involving a third electron in the occupied band. This mechanism can also be viewed as the real space picture of exciton-mediated pairing. Possible realization of this idea leading to strong-coupling, spin-triplet superconductivity in WTe2 and magic-angle graphene will be discussed.

Based on works with Valentine Crepel and Kevin Slagle:
[1] V. Crepel and L. Fu, arXiv:2012.08528
[2] V. Crepel and L. Fu, arXiv:2103.12060
[3] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)

Experimental metaphysics is the study of how empirical results can reveal indisputable facts about the fundamental nature of the world, independent of any theory. It is a field born from Bell’s 1964 theorem, and the experiments it inspired, proving the world cannot be both local and deterministic. However, there is an implicit assumption in Bell’s theorem, that the observed result of any measurement is absolute (it has some value which is not ‘relative to its observer’). This assumption may be called into question when the observer becomes a quantum system (the “Wigner’s Friend” scenario), which has recently been the subject of renewed interest. Here, building on work by Brukner, we derive a theorem, in experimental metaphysics, for this scenario [1]. It is similar to Bell’s 1964 theorem but dispenses with the assumption of determinism. The remaining assumptions, which we collectively call "local friendliness", yield a strictly larger polytope of bipartite correlations than those in Bell's theorem (local determinism), but quantum mechanics still allows correlations outside the local friendliness polytope.  We illustrate this in an experiment in which the friend system is a single photonic qubit [1]. I argue that a truly convincing experiment could be realised if that system were a sufficiently advanced artificial intelligence software running on a very large quantum computer, so that it could be regarded genuinely as a friend. I will briefly discuss the implications of this far-future scenario for various interpretations and modifications of quantum theory.

[1] Kok-Wei Bong, Aníbal Utreras-Alarcón, Farzad Ghafari, Yeong-Cherng Liang, Nora Tischler, Eric G. Cavalcanti, Geoff J. Pryde and Howard M. Wiseman, “A strong no-go theorem on the Wigner’s friend paradox", Nature Physics (2020).

Asymptotically safe gravity is one of the most conservative approaches to quantum gravity. It relies on the framework of quantum field theory and the Wilsonian renormalization group. Recently, questions and open issues have been discussed both within and outside its community. This week, instead of a seminar, we will have a debate between John Donoghue ("A Critique of the Asymptotic Safety Program", arXiv:1911.02967) and Roberto Percacci ("Critical reflections on asymptotically safe gravity", arXiv:2004.06810), who will critically discuss the status of the field, and highlight its strengths and challenges. 

The X-ray source Cygnus X-1 was discovered by sounding rockets in 1964 and is perhaps the oldest and best known "black hole candidate".   Its celestial coordinates were poorly known until 1971, when simultaneous radio flares and X-ray flares were observed which enabled the X-ray source to be associated with a 9th magnitude O-star known as HDE 226868.  This star was subsequently shown to be a single-lined spectroscopic binary with an orbital period of about 5.6 days.  However, owing to difficulties with measuring the system geometry and the distance to the source, the mass of the dark companion remained elusive.  In 1974, Stephen Hawking and Kip Thorne famously made a wager on the nature of the dark companion in Cygnus X-1, with Hawking wagering that the dark companion was not a black hole.  Eventually the consensus was that Cygnus X-1 does indeed contain a black hole, and Hawking conceded the bet in 1990.    In the following years many estimates for the black hole mass appeared in the literature, and most of them had large uncertainties, mainly owing to the difficulty of measuring the distance to the source.  In this talk I will describe how we were able to use VLBI radio observations to measure a precise distance to the source, and how, in turn, this precise distance allowed us to obtain precise masses for the component stars in Cygnus X-1.  Using the refined distance and geometry of the binary, it is possible to measure the relativistic spin parameter a* of the black hole using the X-ray continuum fitting technique.  We find that the black hole spin is nearly maximal with  a* > 0.9985 (3σ).

Recent work has defined what it means for one quantum system to simulate the full physics of another, and demonstrated that—within a very demanding definition of simulation —there exist families of local Hamiltonians that are universal, in the sense that they can simulate all other quantum Hamiltonians. This rigorous mathematical framework of Hamiltonian simulation not only gave a theoretical foundation for describing analogue Hamiltonian simulation. It also unified many previous Hamiltonian complexity results, and implied new ones. It has even found applications in constructing the first rigorous holographic dualities between local Hamiltonians, providing richer toy models of AdS/CFT duality in quantum gravity.

All previous constructions of universal Hamiltonians have relied heavily on using perturbation gadgets, and constructing complicated ‘chains’ of simulations to prove that simple models are indeed universal. In recent work we developed a new method for proving universality. Unlike perturbation- gadget approaches, this directly leverages the ability to encode computation into the ground states of QMA-hard Hamiltonians. With this technique we are able to derive necessary and sufficient complexity-theoretic conditions characterising universal Hamiltonians. We also use our new simulation method to provide a simple construction of two new universal models. Both of these are translationally invariant systems in 1D, and we show that one of these constructions is efficient in terms of the number of spins in the universal construction (but not in terms of the norm of the simulating Hamiltonian). This is the first translationally invariant universal model which is efficient in terms of system size overhead.

Based on joint work with Stephen Piddock, Johannes Bausch and Toby Cubitt (arXiv:2003.13753, arXiv:2101.12319)

Indigenous wellness and higher education in Canada, through the creation of Indian Residential Schools, has a dark history and has left a legacy of intergenerational trauma for Indigenous peoples. Currently, the Truth and Reconciliation Commission’s Final Report (2015) provides  a timely context for systemic change that can improve the lives of Indigenous individuals and provide healing to Indigenous communities. This presentation addresses Indigenous academic strengths and challenges in Canada and provides practical implications of implementing decolonial change in higher education settings. Examples from Dr. Stewart’s community-based Indigenous ethics and educational research provide concrete illustrations of issues such as racism, oppression, cultural identity, tensions between Western and Indigenous worldviews, and the importance of traditional knowledges.

The dark photon is a well-motivated extension of the Standard Model which can mix with the regular photon. This mixing is enhanced whenever the dark photon mass matches the primordial plasma frequency, leading to resonant conversions between photons and dark photons. These conversions can produce observable cosmological signatures, including distortions to the cosmic radiation background. In this talk, I will discuss a new analytic formalism for these conversions that can account for the inhomogeneous distribution of matter in our universe, leading to new and revised limits on the mixing parameter of light dark photons derived from the COBE/FIRAS measurement of the cosmic microwave background spectrum. I will then describe some ongoing work on a dark sector model that can explain the longstanding ARCADE radio background excess through resonant conversions of dark photons.

The vast complexity is a daunting property of generic quantum states that poses a significant challenge for theoretical treatments, especially in non-equilibrium setups. Therefore, it is vital to recognize states which are locally less complex and thus describable with (classical) effective theories.

I will discuss how unsupervised learning can detect the local complexity of states. This approach can be used as a probe of scrambling and thermalization in chaotic quantum systems or to assign the local complexity of density matrices in open setups without knowing the corresponding Hamiltonian or Liouvillian. The analysis actually allows for the reconstruction of Hamiltonian operators or even noise-type that might be contaminating the measurements. Our approach is an ideal diagnostics tool for data obtained from (noisy) quantum simulators because it requires only practically accessible local observations. For example, it would be perfectly suited to detect the many-body localization (MBL) transition or integrability effects from the experimental snapshots obtained with cold atoms.

If time permits, I will mention other ways to detect properties of MBL transition in weakly open and driven setups and the advantages of such an unconventional approach.

M. Schmitt and Z. Lenarcic, arXiv:2102.11328.

Z. Lenarcic, O. Alberton, A. Rosch and E. Altman, PRL 125, 116601 (2020).

We show that bulk operators lying between the outermost extremal surface and the asymptotic boundary admit a simple boundary reconstruction in the classical limit. This is the converse of the Python's lunch conjecture, which proposes that operators with support between the minimal and outermost (quantum) extremal surfaces - e.g. the interior Hawking partners - are highly complex. Our procedure for reconstructing this "simple wedge" is based on the HKLL construction, but uses causal bulk propagation of perturbed boundary conditions on Lorentzian timefolds to expand the causal wedge as far as the outermost extremal surface. As a corollary, we establish the Simple Entropy proposal for the holographic dual of the area of a marginally trapped surface as well as a similar holographic dual for the outermost extremal surface. We find that the simple wedge is dual to a particular coarse-grained CFT state, obtained via averaging over all possible Python's lunches. An efficient quantum circuit converts this coarse-grained state into a "simple state" that is indistinguishable in finite time from a state with a local modular Hamiltonian. Under certain circumstances, the simple state modular Hamiltonian generates an exactly local flow; we interpret this result as a holographic dual of black hole uniqueness.