Talks

In quantum spin systems, the existence of a spectral gap above the ground state has strong implications for the low-energy physics. We survey recent results establishing spectral gaps in various frustration-free spin systems by verifying finite-size criteria. The talk is based on collaborations with Abdul-Rahman, Lucia, Mozgunov, Nachtergaele, Sandvik, Yang, Young, and Wang.

I will explain how dark energy in cosmology could arise from the

noisy diffusion of energy from the low energy degrees of freedom of matter (described in terms of QFT)

to the fundamental Planckian granularity (expected from quantum gravity). This

perspective leads to a natural model resolving the fine tuning problem associated to the small

value of the cosmological constant. However, recent observations suggest that the dark energy

component in our universe might not be constant and should  instead have grown from the recombination time to the present.

I will present new ideas suggesting a possible explanation within the same framework.

Analytic renormalisation "à la Speer" using a multivariable approach typically leads to meromorphic germs in several variables whose poles are linear.  In particular,  Feynman integrals, multizeta functions and their generalisations, namely  discrete sums on cones and discrete sums associated with trees give rise to meromorphic germs at zero with linear poles. We shall present  a multivariable renormalisation scheme which amounts to a minimal subtraction scheme in several variables. It preserves locality in so far as the  evaluation at poles is expected to factor  on functions with independent sets of variables. Inspired by Speer, we shall discuss a class of generalised evaluators that do the job. Using a theory of  Laurent expansions  on meromorphic germs with linear poles at zero, we shall relate these generalised evaluators to the geometry of cones.

This talk is based on joint work with Pierre Clavier, Li Guo and Bin Zhang.

Many of the most mysterious phenomena in condensed matter physics involve systems near quantum phase transitions where the interplay of quenched disorder and strong interactions likely plays an essential role. Examples include the appearance of "anomalous" 2d metallic phases and the sharing of critical exponents between seemingly different quantum Hall plateau transitions. However, few organizing principles have been developed for understanding quantum critical systems with interactions and disorder, and analytically tractable models have proven rare. In this talk, I will describe some of the first examples of quantum critical theories in 2d characterized by finite disorder and interaction strengths, focusing on particular examples of quenched disorder in systems of (i) Dirac fermions coupled to an emergent gauge field (QED3) and (ii) scalar bosons at their Wilson-Fisher fixed point. Both of these examples exhibit universal features not found together in systems with interactions or disorder alone, such as vanishing density of states, finite DC conductivities, and novel critical exponents.