Scientific Series

In the context of the AdS(4)/BCFT(3) correspondence, we study the holographic entanglement entropy for spatial regions having arbitrary shape. An analytic expression for the subleading term with respect to the area law is discussed. When the bulk spacetime is a part of AdS(4),
this formula becomes the Willmore functional with a proper boundary term evaluated on the minimal surface viewed as a submanifold of the three dimensional flat Euclidean space with a boundary. 
Numerical checks of this formula are performed through a code which allows to construct minimal area surfaces anchored to generic curves. For some simple regions like infinite strips and disks, analytic results are obtained and they confirm the general expression for the subleading term. In particular, when the spatial region contains corners adjacent to the boundary, a logarithmic divergence occurs whose coefficient is determined by a so-called corner function which depends on the boundary conditions. An analytic expression for the holographic corner function and its checks are also discussed.

The localization theorem, which has played a central role in representation theory since its discovery in the 1980s, identifies a regular block of Category O for a semisimple Lie algebra with certain D-modules on its flag variety. In this talk we will explain work in progress which produces a similar picture for the Virasoro algebra and more generally for affine W-algebras. Some new purely algebraic input is (i) a version of the Feigin-Fuchs duality between Verma modules for Vir at central charges c and 26 - c, which applies to all smooth representations and other affine W-algebras, and (ii) a linkage principle for representations in category O of a W-algebra. As geometric input, we will explain how to (i) adapt the Beilinson-Drinfeld construction of vertex algebras via factorization spaces to also produce representations and in particular (ii) develop a factorizable version of affine Borel--Weil--Bott.  

Gravitational lensing has long served as a unique probe of the growth of structure, which is sensitive on large scales to the properties of dark energy and gravity.  In particular, lensing is instrumental in forming the statistic E_G, which is constructed to measure the growth rate of structure in a way independent of galaxy clustering bias.  Measurements of E_G using both CMB lensing and galaxy lensing have proliferated, but new challenges await as the data from upcoming surveys become more precise.  One such challenge is the bias on E_G due to the inhomogeneous magnification of galaxies.  In this talk, we will discuss how to identify this bias and calibrate it to remove from survey data.  We also consider a new tracer of gravitational lensing, namely upcoming 3D line intensity maps of emission lines such as the 21 cm line from neutral hydrogen.  Previous considerations of this new probe have assumed the flat-sky approximation, valid over small areas, where all light rays are assumed to come from the same direction.  We will present our extension of this treatment to the full-sky case which will be needed for large-area, 21 cm surveys such as HIRAX.  We will then discuss how this enhancement could improve intensity mapping probes of gravity.

Studying the usefulness of resources can be formalized via the framework of a resource theory. However, the complete answer to the question whether a certain resource is more useful than another one is often hard to find in many of the numerous applications of the framework. Approximate answers can be found by identifying so-called monotones—measures of "resourcefulness". I will present several generic constructions of monotones, of which many monotones known in the literature are concrete examples of. These constructions provide a way to relate monotones in different resource theories, thus enabling for the translation of results between them.

Simplicial complexes naturally describe discrete topological spaces. When their links are assigned a length they describe discrete geometries. As such simplicial complexes have been widely used in quantum gravity approaches that involve a discretization of spacetime. Recently they are becoming increasingly popular to describe complex interacting systems such a brain networks or social networks. In this talk we present non-equilibrium statistical mechanics approaches to model large simplicial complexes. We propose the simplicial complex model of Network Geometry with Flavor (NGF), we explore the hyperbolic nature of its emergent geometry and their relation with Tree Tensor Networks. Finally we reveal the rich interplay between Network Geometry with Flavor and dynamics. We investigate the percolation properties of NGF using the renormalization group finding KTP and discontinuous phase transitions depending on the dimensionality simplex. We also comment on the synchronization properties of NGF and the emergence of frustrated synchronization.

 One of the most important discoveries of the 20th century has been the finding of neutrino oscillations. That phenomena implies that neutrinos are massive and shows the existence of physics beyond the standard model. Fundamental questions associated to this discovery are: what are the absolute neutrino masses? and what is their hierarchy? In this talk I will discuss how to use cosmological observables to answer these questions. I will first show one of the predictions of the Big Bang theory: the existence of a cosmic neutrino background. I will then present the effects that it introduces on several cosmological observables such as the matter power spectrum, halo/galaxy properties, cluster counts, halo/galaxy clustering and cosmic voids. I will show how to use these effects to weigh neutrinos. I will emphasize the importance of having accurate theory predictions, and to search for new observables, in order to achieve a 5-sigma detection of the minimum sum of the neutrino masses.

In quanum physics, the von Neumann entropy usually arises in i.i.d settings, while single-shot settings are commonly characterized by smoothed min- or max-entropies. In this talk, I will discuss new results that give single-shot interpretations to the von Neumann entropy under appropriate conditions. I first present new results that give a single-shot interpretation to the Area Law of entanglement entropy in many-body physics in terms of compression of quantum information on the boundary of a region of space. Then I show that the von Neumann entropy governs single-shot transitions whenever one has access to arbitrary auxiliary systems, which have to remain invariant in a state-transition ("catalysts"), as well as a decohering environment. Getting rid of the decohering environment yields the "catalytic entropy conjecture", for which I present some supporting arguments.

If time permits, I also discuss some applications of these result to thermodynamics and speculate about consequences for quantum information theory and holography.

I will present recent results (with Zhen Bi) on novel quantum criticality and a possible field theory duality in 3+1 spacetime dimensions. We describe several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1-D.   We present situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. We exhibit the possibility - which we dub “unnecessary quantum critical points” - of stable generic continuous phase transitions within the same phase. We present examples of interaction driven band-theory- forbidden continuous phase transitions between two distinct band insulators. The understanding we develop leads us to suggest an interesting possible 3 + 1-D field theory duality between SU(2) gauge theory coupled to one massless adjoint Dirac fermion and the theory of a single massless Dirac fermion augmented by a decoupled topological field theory.

Many-body localization generalizes the concept of Anderson localization (i.e. single particle localization) to isolated interacting systems, where many-body eigenstates in the presence of sufficiently strong disorder can be localized in a region of Hilbert space even at nonzero temperature. This is an example of ergodicity breaking, which manifests failure of thermalization or more specifically the break down of eigenstate-thermalization hypothesis.

In this talk, I enquire into the quasi many-body localization in topologically ordered states of matter, revolving around the case of Kitaev toric code on the ladder geometry, where different types of anyonic defects carry different masses induced by environmental errors.  Our study verifies that the presence of anyons generates a complex energy landscape solely through braiding statistics, which suffices to suppress the diffusion of defects in such clean, multicomponent anyonic liquid. This nonergodic dynamics suggests a promising scenario for investigation of quasi many-body localization.  Our results unveil how self-generated disorder ameliorates the vulnerability of topological order away from equilibrium. This setting provides a new platform which paves the way toward impeding logical errors by self-localization of anyons in a generic, high energy state, originated exclusively in their exotic statistics.

We propose to generalise classical maximum likelihood learning to density matrices. As the objective function, we propose a quantum likelihood that is related to the cross entropy between density matrices. We apply this learning criterion to the quantum Boltzmann machine (QBM), previously proposed by Amin et al. We demonstrate for the first time learning a quantum Hamiltonian from quantum statistics using this approach. For the anti-ferromagnetic Heisenberg and XYZ model we recover the true ground state wave function and Hamiltonian. The second contribution is to apply quantum learning to learn from classical data. Quantum learning uses in addition to the classical statistics also quantum statistics for learning. These statistics may violate the Bell inequality, as in the quantum case. Maximizing the quantum likelihood yields results that are significantly more accurate than the classical maximum likelihood approach in several cases. We give an example how the QBM can learn a strongly non-linear problem such as the parity problem. The solution shows entanglement, quantified by the entanglement entropy.

The role of coherence in quantum thermodynamics has been extensively studied in the recent years and it is now well-understood that coherence between different energy eigenstates is a resource independent of other thermodynamics resources, such as work. A fundamental remaining open question is whether the laws of quantum mechanics and thermodynamics allow the existence a "coherence distillation machine", i.e. a machine that, by possibly consuming work, obtains pure coherent states from mixed states, at a nonzero rate. This question is related to another fundamental question: Starting from many copies of noisy quantum clocks which are (approximately) synchronized with a reference clock, can we distill synchronized clocks in pure states, at a non-zero rate? In this paper we study quantities called "coherence cost" and "distillable coherence", which determine the rate of conversion of coherence in a standard pure state to general mixed states, and vice versa, in the context of quantum thermodynamics. We find that the coherence cost of any state (pure or mixed) is determined by its Quantum Fisher Information (QFI), thereby revealing a novel operational interpretation of this central quantity of quantum metrology. On the other hand, we show that, surprisingly, distillable coherence is zero for typical (full-rank) mixed states. Hence, we establish the impossibility of coherence distillation machines in quantum thermodynamics, which can be compared with the impossibility of perpetual motion machines or cloning machines. To establish this result, we introduce a new additive quantifier of coherence, called the "purity of coherence", and argue that its relation with QFI is analogous to the relation between the free and total energies in thermodynamics.