Talks

The precise determination of the entanglement of an interacting quantum many-body systems is now appreciated as an indispensable tool to identify the fundamental character of the ground state of such systems. This is particularly true for unconventional ground states harbouring non-local topological order or so-called quantum spin liquids that evade a standard description in terms of correlation functions. With the entanglement entropy emerging as one of the central measures of entanglement, recent progress has focused on a precise characterization of its scaling behaviour, in particular in the determination of (subleading) corrections to the prevalent boundary-law. 

In the past years, much progress has been made for certain spin, bosonic, and even fermionic quantum many-body systems. However, a large class of interacting models is thought to be exempt from numerical studies due to the fermion sign problem. At its heart, it occurs when the statistical weights in the simulation are positive and negative resulting in an exponential scaling of the algorithm instead of a polynomial one. In this work, we study the connection of the sign problem and the entanglement entropy using Determinantal Quantum Monte Carlo, the method of choice for unbiased, large-scale simulations of fermionic systems. We show that there is a strong correlation between the behavior of the entanglement entropy and the sign problem and that the particular structure of the ‘observable’ entanglement entropy to some extent allows to handle the sign problem much better than for usual correlation functions.

Bell inequalities bound the strength of classical correlations arising between outcomes of measurements performed on subsystems of a shared physical system. The ability of quantum theory to violate Bell inequalities has been intensively studied for several decades. Recently, there has been an increased interest in studying physical correlations beyond the scenario of Bell inequalities, to more general network structures involving many sources of physical states and observers that may be measuring on subsystems of independent states. Much less is known about the nature of physical correlations in networks as compared to standard Bell inequalities. In this talk we will discuss the motivation and interest for studying such network correlations, review the recent progress in understanding such networks, and discuss the many open questions and new possible directions for research on this topic.

I will discuss ongoing work developing Hamiltonian truncation methods for studying strongly-coupled IR physics originating from a perturbed UV conformal field theory. This method uses a UV basis of conformal Casimir eigenstates, which is truncated at some maximum Casimir eigenvalue, to approximate the low energy spectrum of the IR theory. So far, such methods have been limited to theories in 2D, and I will present a new framework for generalizing this approach to higher dimensions. Focusing specifically on the case of scalar fields in 3D, I will then show tests of this framework by comparing with known analytic results at weak coupling and in the O(N) model at large-N, before discussing the possible application to strongly-coupled systems like the 3D Ising model.