Talks

Understanding entanglement in QFTs is a challenging topic that involves many aspects. One important probe for this is the modular (or entanglement) Hamiltonian, which is closely related to the Unruh effect. We determine this operator for the chiral fermion at finite temperature on the circle using complex analysis, and show that it exhibits surprising new features. This simple system illustrates how a modular flow can transition from complete locality to complete non-locality as a function of temperature, thus bridging the gap between previously known limits. We also derive the first exact results for the entanglement and relative entropies of this system for the different spin sectors. Based on [1905.05768,1906.02207].

In this talk I will report on recent progress in building QFT models on causal sets. The framework I'm using is that of perturbative algebraic quantum field theory (pAQFT). It was developed for rigorous study of perturbative QFT in the continuum, but can also be applied in the situation where spacetime is replaced by a discrete structure. Causality plays a key role in pAQFT, so it is natural to apply it to causets. Construction of models in this framework is purely algebraic and one does not need to specify a state or a Hilbert space representation until the final step, in which correlation functions are computed.

 In the 90s Turaev, Viro, Barrett and Westbury constructed a (2+1)D state sum TQFT associated to any fusion category. The associated phases of matter were popularized by Kiteav, Levin and Wen and are now central  examples in condensed matter physics and quantum information theory.

Despite the importance of these phases, many of the computational techniques for working with fusion categories have not percolated into condensed matter physics. Many of these techniques are "folk theorems"
and have not appeared in the literature in a digestible form.

Jacob Bridgeman and myself have spent the last two years extracting these computational techniques from Corey Jones, and have been using them to understand defects in Levin-Wen phases. Our papers 1806.01279,
1810.09469, 1901.08069, 1907.06692 document the development of our understanding, and demonstrate how to do physically relevant fusion category computations.