Title: Fractons electrodynamics and geometry.
Abstract: Generic gapless fracton systems are characterized by the conservation of certain global charge and its higher momenta. In particular, the simplest case is given by the simultaneous conservation of scalar and dipole charges. Actually, this feature is captured by a generalized continuity equation, where the fracton current is a symmetric tensor. Such type of conservation law can be derived from a non-standard gauge principle, with the (scalar) charge density and current coupling to scalar and symmetric gauge potentials respectively. In my talk I will discuss the similarities of this system with ‘gravity theories’ once energy and momentum conservation is requested, and using standard techniques for gauging space-time symmetries I will derive a fully covariant symmetric gauge fields electrodynamic theory. In addition, I will use the formalism to extract the matter fields Ward identities in case of non-dynamical.
Title: Geometric complexity in quantum matter: intrinsic sign problems in topological phases
Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence, and the geometric origin, of intrinsic sign problems in a broad class of topological phases in 2+1 dimensions. Within this class, these results exclude the possibility of ‘stoquastic’ Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on Phys. Rev. Research 2, 043032 and 033515.
Title: Witnesses of non-classicality beyond quantum theory
Abstract: The theory of quantum computation has brought us rapid technological developments, together with remarkable improvements in how we understand quantum theory. I will describe the foundations of a programme to extend the quantum theory of computation beyond quantum theory itself, and explain a recent application of this new approach to the problem of testing quantum effects in gravity.
Dung Xuan Nguyen
Title: Graviton excitations in Fractional Quantum Hall systems
Abstract: In this talk, I will provide the historical review of magneto-roton excitation, which is the gapped neutral excitation in the Lowest Landau Level.
The magneto-roton mode has spin-2 and can be considered as massive graviton mode in 2+1D . This spin-2 mode plays a central role in the physics of FQH. In the current literature, the spin-2 mode of Jain’s sequences near filling fraction 1/2 can be thought of as the shear deformation of the composite fermion Fermi surface. In this talk, I will show that for Jain’s sequences near filling fraction 1/4, there will be an extra massive graviton mode. The extra mode was proposed in our recent work on the Dirac composite fermion theory of general Jain’s sequences in order to satisfy the Haldane bound of the static structure factor. The extra mode was confirmed numerically recently. I will briefly discuss our physical interpretation of the new massive graviton mode. If time allows, I will describe the experimental setup that can detect the graviton modes.
Title: Topological String Theory and Condensed Matter Physics
Abstract: Recently, the relations between topological string theories and Hofstadter models are found. The topological string theory is a type of string theory which is known as a toy model of string theory. The Hofstadter model describes an electron on two dimensional lattice with a perpendicular magnetic flux. Its band spectrum draws an interesting pattern, called as Hofstadter butterfly. In this talk, firstly I will explain some aspects of (topological) string theories and Hofstadter models. After that, I will show that the topological string draws Hofstadter butterfly. This correspondence allows us to use the knowledge of condensed matter physics to investigate the topological string theory, and vice versa.
Title: The gravitational spin Hall effect of light
Abstract: Spin Hall effects are well known in optics and condensed matter physics, where they describe the spin-dependent dynamics of localized wave packets. In general relativity, the propagation of electromagnetic waves in vacuum is often described by using the geometrical optics approximation, which predicts that wave rays follow null geodesics. However, this model is valid only in the limit of infinitely high frequencies. At large but finite frequencies, diffraction can still be negligible, but the ray dynamics becomes affected by the evolution of the wave polarization. This is known as the gravitational spin Hall effect of light. In close analogy with the spin Hall effect of light in optics, I will briefly present the main steps of a covariant derivation of the polarization-dependent ray equations describing the gravitational spin Hall effect of light. I will also discuss the relation of these equations with the well-known MPD equations, as well as the observer dependence of the position of massless spinning particles.
Title: Anyons and the Double Copy
Abstract: The double copy is an established relationship between gauge theories and gravity, which can be roughly summarised as GR ~ (Yang-Mills)^2. In this talk, I will discuss surprising aspects of the double copy in (2+1)-dimensional planar physics. To set the scene, I will give a brief overview of the double copy in four dimensions before describing what this teaches us about lower dimensions. We will learn that we are naturally led to a double copy involving topologically massive theories in three dimensions, which includes some interesting implications for planar physics, such as the double copy of anyons and the Aharonov-Bohm phase.
Title: Entanglement of quantum systems through gravity and the nature of the gravitational field beyond quantum theory
Abstract: Recently, table-top experiments involving massive quantum systems have been proposed to test the interface of quantum theory and gravity. In particular, the crucial point of the debate is whether it is possible to conclude anything on the quantum nature of the gravitational field, provided that two quantum systems become entangled due to solely the gravitational interaction. In my talk, I will first review a thought experiment thanks to which one can argue that, in order to understand how the system may become entangled with other massive systems via gravitational interactions, it must be thought of as being entangled with its own Newtonian-like gravitational field. I will then show that, by introducing the framework of Generalised Probabilistic Theories (GPTs) to the study of the nature of the gravitational field, one can systematically study all theories compatible with the detection of entanglement generated via the gravitational interaction between two non-classical systems. Assuming that such gravitationally mediated entanglement is observed, I will formulate a no-go theorem stating that gravity cannot simultaneously satisfy the following conditions i) the two non-classical systems are independent subsystems, ii) the gravitational field is a physical degree of freedom which mediates the interaction and iii) the gravitational field is classical. Moreover, I will argue that conditions i) and ii) should be met, and hence that the gravitational field is non-classical. However, I will motivate that non-classicality does not imply that the gravitational field is quantum.