Talks

Recent studies of highly frustrated antiferromagnets (AFMs) have demonstrated the qualitative impact of virtual, longer-range singlet excitations on the effective RVB tunneling parameters of the low energy sector of the problem [1,2]. Here, I will discuss the current state of affairs on the RVB description of the spin-1/2 kagome AFM, and present new results that settle a number of issues in this problem [3].

[1] I. Rousochatzakis, Y. Wan, O. Tchernyshyov, and F. Mila, PRB 90,

100406(R) (2014)

[2] A. Ralko and I. Rousochatzakis, PRL 115, 167202 (2015) [3] in preparation.

What can we say about the spectra of a collection of microscopic variables when only their coarse-grained sums are experimentally accessible? In this paper, using the tools and methodology from the study of quantum nonlocality, we develop a mathematical theory of the macroscopic fluctuations generated by ensembles of independent microscopic discrete systems. We provide algorithms to decide which multivariate gaussian distributions can be approximated by sums of finitely-valued random vectors. We study non-trivial cases where the microscopic variables have an unbounded range, as well as asymptotic scenarios with infinitely many macroscopic variables. From a foundational point of view, our results imply that bipartite gaussian states of light cannot be understood as beams of independent d-dimensional particle pairs. It is also shown that the classical description of certain macroscopic optical experiments, as opposed to the quantum one, requires variables with infinite cardinality spectra.

Since the Higgs, the LHC has offered no discoveries despite a sweeping hunt for new resonances. However, many well-motivated new physics models would not turn up in resonance searches, but could instead be uncovered in existing and forthcoming LHC data, by searching for novel angular distributions of Standard Model particles. I will show that in the upcoming years at the LHC, (1) through radiative corrections, dark matter can turn up in dilepton scattering angles in the parametric regions where it would elude conventional missing energy-based searches; the scattering patterns can reveal dark matter's mass, self-conjugation property, spin, and chirality of interactions, (2) through tree level interference, leptoquarks may emerge in dilepton scattering angles long before they would in dedicated direct searches; these angular measurements would also overtake the excellent sensitivities of low-energy precision measurements of atomic parity violation, and (3) Higgs Yukawa couplings to light quarks of the size of the bottom Yukawa could be measured using the Higgstrahlung scattering angle.

We apply the recently suggested strategy to lift state spaces and operators for (2+1)-dimensional topological quantum field theories to state spaces and operators for a (3+1)-dimensional TQFT with defects. We start from the (2+1)-dimensional Turaev-Viro theory and obtain a state space, consistent with the state space expected from the Crane-Yetter model with line defects. This work has important applications for quantum gravity as well as the theory of topological phases in (3+1) dimensions.