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The Fermi-Hubbard model is of fundamental importance in condensed-matter physics, yet is extremely challenging to solve numerically. Finding the ground state of the Hubbard model using variational methods has been predicted to be one of the first applications of near-term quantum computers. In this talk, I will discuss recent work which carried out a detailed analysis and optimisation of the complexity of variational quantum algorithms for finding the ground state of the Hubbard model, including extensive numerical experiments for systems with up to 12 sites. The depth complexities we find are substantially lower than previous work. If our numerical results on small lattice sizes are representative of the somewhat larger lattices accessible to near-term quantum hardware, they suggest that optimising over quantum circuits with a gate depth less than a thousand could be sufficient to solve instances of the Hubbard model beyond the capacity of classical exact diagonalisation. I will also discuss a proof-of-principle implementation on Rigetti quantum computing hardware.

The talk is based on joint work with Chris Cade, Lana Mineh and Stasja Stanisic ( arXiv:1912.06007 , arXiv:2006.01179 ).

Gravitational waves provide a unique way to study the universe. From the initial direct detection of coalescing black holes in 2015, to the ground-breaking multimessenger observations of coalescing neutron stars in 2017, and continuing with the now routine detection of merging stellar remnants, gravitational wave astronomy has quickly matured into a key aspect of modern physics. After briefly discussing what we've begun to learn from the new gravitational-wave transient catalog published by the LIGO, Virgo, and KAGRA collaborations (GWTC-2), I will discuss novel tests of fundamental physics GWs enable. In particular, I will focus on our current understanding of matter effects during the inspiral of compact binaries and matter at supranuclear densities, including possible phase transitions, through tests of neutron star structure. Detailed knowledge of dynamical interactions between coalescing stars, observations of extreme relativistic astrophysical systems, terrestrial experiments, and nuclear theory provide complementary views of fundamental physics. I will show how combining aspects from all these will improve our understanding of dense matter through the example of how we can determine whether newly observed objects are neutron stars or black holes.

The standard model of cosmology is built upon on a series of propositions on how the early, intermediate, and late epochs of the Universe behave. In particular, it predicts that dark energy and dark matter currently pervades the cosmos. Understanding the properties of the dark sector is plausibly the biggest challenge in theoretical physics. There is, however, a broad assumption in cosmology that the Universe on its earlier stages is fully understood and that discrepancies between the standard model of cosmology and current data are suggestive of distinct dark energy properties. Uncertainties on the validity of this hypothesis are not usually taken into account when forecasting survey capabilities, even though our investigations might be obfuscated if the intermediate and early Universe did behave abnormally. In this colloquium, I propose a program to investigate dark energy and earlier aspects of our Universe simultaneously, through space missions in the 2020s in combination with ground-based observatories. This program will help guide the strategy for the future LSST and WFIRST supernovae and weak lensing surveys. My investigations on how properties of the early and intermediate Universe affect inferences on dark energy (and vice-versa) will also support community understanding of how future missions can be employed to test some of the core hypotheses of the standard model of cosmology.

Flat bands in Moire superlattices are emerging as a fascinating new playground for correlated electron physics. I will present the results of several studies inspired by these developments. First, I will address the question of whether superconductivity is possible even in the limit of a perfectly flat band. Then, I will discuss transport properties of a spin-polarized superconductor in the limit of zero spin-orbit coupling, where the topological structure of the order parameter space allows for a new dissipation mechanism not known from conventional superconductors. If time allows, I will also discuss the interpretation of new measurements of the electronic compressibility in twisted bilayer graphene, indicating a cascade of symmetry-breaking transitions as a function of the density of carriers in the system. 

References:

https://arxiv.org/abs/2006.10073

https://arxiv.org/abs/1912.08848

https://arxiv.org/abs/1912.06150

The compatibility-hypergraph approach to contextuality (CA) and the contextuality-by-default approach (CbD) are usually presented as products of entirely different views on how physical measurements and measurement contexts should be understood: the latter is based on the idea that a physical measurement has to be seen by a collection of random variables, one for each context containing that measurement, while the imposition of the non-disturbance condition as a physical requirement in the former precludes such interpretation of measurements. The aim of our work is to present both approaches as entirely compatible ones and to introduce in the compatibility-hypergraph approach ideas which arises from contextuality-by-default. We

introduce in CA the non-degeneracy condition, which is the analogous of consistent connectedness (an important concept from CbD), and prove that this condition is, in general, weaker than non-disturbance. The set of non-degenerate behaviours defines a polytope, therefore one can characterize non-degeneracy using a finite set of linear inequalities. We introduce extended contextuality for behaviours and prove that a behaviour is non-contextual in the standard sense if and only if it is non-degenerate and non-contextual in the extended sense. Finally, we use extended scenarios and behaviours to shed new light on our results.

Dual gravitational charges (DGCs) have been originally computed in the first-order formalism by means of covariant phase space methods using tetrad variables. I show i) why DGCs do not arise using the metric variables and ii) how they can be set to zero by exploiting the freedom to add exact 3-forms to the symplectic potential.

Without exploiting that freedom, DGCs can be understood as Hamiltonian charges associated to the Kosmann variation. I then discuss the implications of this observation for asymptotic symmetries and comment about subleading contributions thereof.

Finally, I also show that DGCs can be equally derived by means of cohomological methods. In this case, DGCs depends on the order of the Lagrangian: they exist only in the first-order formalism.

Borcherds Kac-Moody (BKM) algebras are a generalization of familiar Kac-Moody algebras with imaginary simple roots. On the one hand, they were invented by Borcherds in his proof of the monstrous moonshine conjectures and have many interesting connections to new moonshines, number theory and the theory of automorphic forms. On the other hand, there is an old conjecture of Harvey and Moore that BPS states in string theory form an algebra that is in some cases a BKM algebra and which is based on certain signatures of BKMs observed in 4d threshold corrections and black hole physics. I will talk about the construction of new BKMs superalgebras arising from self-dual vertex operator algebras of central charge 12, and comment on their relation to physical string theories in 2 dimensions. Based on work with N. Paquette, D. Persson, and R. Volpato.

Millisecond Pulsars (MSPs) have become reliable and
extremely stable workhorses of modern astronomy and physics.  The
North American Nanohertz Observatory for Gravitational Waves, or
NANOGrav, has been observing growing numbers of these systems for over
15 years, and the data look great.  High precision timing of almost 80
MSPs has provided unprecedented sensitivity to the gravitational wave
Universe at nHz-frequencies, where our upper limits are already
constraining the population of super-massive black hole binaries.  But
our sensitivity is increasing each year as we continue to add MSPs to
our timing array and develop new techniques to remove systematics due
to the interstellar medium and the uncertain solar system ephemerides.
Meanwhile, though, our observations provide a wide variety of
astrophysics, such as new neutron star mass measurements and
constraints of the dense matter equation of state.

To any vertex algebra one can attach in a canonical way a certain Poisson variety, called the associated variety. Nilpotent Slodowy slices appear as associated varieties of admissible (simple) W-algebras. They also appear as Higgs branches of the Argyres-Douglas theories in 4d N=2 SCFT’s. These two facts are linked by the so-called Higgs branch conjecture. In this talk I will explain how to exploit the geometry of nilpotent Slodowy slices to study some properties of W-algebras whose motivation stems from physics. This is a joint work with Tomoyuki Arakawa and Jethro van Ekeren (still in preparation).

A standard account of the measurement chain in quantum mechanics involves a probe (itself a quantum system) coupled temporarily to the system of interest. Once the coupling is removed, the probe is measured and the results are interpreted as the measurement of a system observable. Measurement schemes of this type have been studied extensively in Quantum Measurement Theory, but they are rarely discussed in the context of quantum fields and still less on curved spacetimes. 

In this talk I will describe how measurement schemes may be formulated for quantum fields on curved spacetime within the general setting of algebraic QFT. This allows the discussion of the localisation and properties of the system observable induced by a probe measurement, and the way in which a system state can be updated thereafter. The framework is local and fully covariant, allowing the consistent description of measurements made in spacelike separated regions. Furthermore, specific models can be given in which the framework may be exemplified by concrete calculations.

I will also explain how this framework can shed light on an old problem due to Sorkin concerning "impossible measurements" in which measurement apparently conflicts with causality.

The talk is based on work with Rainer Verch [Leipzig], (Comm. Math. Phys. 378, 851–889(2020), arXiv:1810.06512; see also arXiv:1904.06944 for a summary) and a recent preprint arXiv:2003.04660 with Henning Bostelmann and Maximilian H. Ruep [York].