Talks

In this talk, I will present our latest results on the development of algorithms for computer simulations based on tensor network states (TNS). The major part of this talk is concerned with finite projected entangled pair states (PEPS) in 2D: I will discuss their algorithmic properties as well as their performance for typical benchmark Hamiltonians [1, 2]. A minor part of this talk deals with the question whether TNS methods can be useful for density functional theory (DFT).

[1] M. Lubasch, J. I. Cirac, and M.-C. Ba\~{n}uls, New J. Phys. \textbf{16}, 033014 (2014).

[2] M. Lubasch, J. I. Cirac, and M.-C. Ba\~{n}uls, Phys. Rev. B \textbf{90}, 064425 (2014).

I will discuss the Higgs-branch CFT2 dual to string theory on AdS3 x S3 x T4. States localised near the small instanton singularity can be described in terms of vector multiplet variables.  This theory has a planar, weak-coupling limit, in which anomalous dimensions of single-trace composite operators can be calculated. At one loop, the calculation reduces to finding the spectrum of a spin chain with nearest-neighbour interactions. This CFT2 spin chain matches precisely the one that was previously found as the weak-coupling limit of the integrable system describing the AdS3 side of the duality.  In particual I will show that the one-loop dilatation operator in a non-trivial compact subsector corresponds to an integrable spin-chain Hamiltonian. This provides the first direct evidence of integrability on the CFT2 side of the correspondence.

 

Modern numerical methods have revolutionized the practice of science, creating a third discipline between traditional theory and experiment. Perhaps the most widely known and successful technique has been the Monte Carlo method in general, and the Metropolis algorithm in particular. In this talk, I will present a new way of performing unbiased Monte Carlo simulations based on highly-accurate tensor network contractions. The resulting technique inherits the legendary precision of tensor networks without any of the variational bias. From a Monte Carlo point-of-view, the method can be seen as an aggressive multi-sampling technique where each sample may account for the vast majority of the entire partition function resulting a a drastic reduction in sample-to-sample variance (in contrast to standard
configuration-based Monte Carlo, where only a small subset of possible configurations are sampled). The presented results are all classical, though applications to quantum systems and the sign problem will be discussed.

Twin Higgs theories attempt to solve the little hierarchy problem - why has the LHC not yet observed new states stabilising the EW scale? - by introducing a SM-neutral twin sector, related to the SM by an approximate Z_2 symmetry. The physical Higgs is then a PNGB mixture from both sectors, and acts as a portal between them. In this talk, I will discuss the cosmology of minimal (“fraternal”) Twin Higgs models. Higgs portal interactions establish thermal equilibrium between the SM and twin sector at high temperatures, giving a thermal history with possibilities for both symmetric dark matter (through a “twin WIMP miracle”), and asymmetric dark matter (from twin QCD states which naturally have GeV-scale masses). More generally, relic abundances of cosmologically stable states place constraints on the parameters of the theory, and twin sector phase transitions need to be considered.

Oscillating signatures in the correlation functions of the primordial density perturbations are predicted by a variety of inflationary models. A theoretical mechanism that has attracted much attention is a periodic shift symmetry as implemented in axion monodromy inflation. This symmetry leads to resonance non-Gaussianities, whose key feature are logarithmically stretched oscillations. Oscillations are also a generic consequence of excited states during inflation and of sharp features in the potential. Oscillating shapes are therefore a very interesting experimental target. 

After giving an overview of the theoretical motivations, I will discuss how to search for these signatures in the CMB. Fast oscillations are difficult to search for with traditional estimation techniques, and I will demonstrate how targeted expansions, that exploit the symmetry properties of the shapes, allow to circumvent these difficulties. As a member of the Planck collaboration, I will discuss the Planck results that have been obtained using these methods in the bispectrum, as well as related results in the power spectrum. Due to their low overlap with other non-gaussian shapes, oscillating bispectrum shapes are not exhaustively constrained and a potential discovery in the CMB is therefore not yet ruled out. 

After a quick review of the Higgs and Coulomb branches of 3d N=4 theories, I'll introduce some simple classes of boundary conditions and explain how they lead to (pairs of) modules for certain (pairs of) quantum algebras. I will focus on abelian theories, for which the relevant boundary conditions/modules can be described using the geometry of (pairs of) hyperplane arrangements. From this, the simplest examples of symplectic-dual modules will arise.