Talks

I will present a new method to constrain the quantum effective action of gravity, inspired by recent results from causal dynamical triangulations (CDT). After a short introduction to CDT, I will start from a parameterisation of the effective action to calculate correlation functions for observable quantities. Matching these correlators to CDT data allows to reverse-engineer the couplings which describe the effective dynamics. As a concrete example, the autocorrelation of spatial volume fluctuations is considered. The comparison to CDT data suggests the existence of non-local interaction terms, which might have interesting phenomenological consequences for the interpretation of dark energy.

It is widely known that topological orders have long-range entangled gapped ground states from which nontrivial properties can be extracted. We introduce a new theoretical framework named the information convex, the (convex) set of reduced density matrices of a subsystem in its lowest energy, to characterize topological orders. (1) As a concrete example, we present the calculated topology dependent structure of information convex in the quantum double models and show it reveals properties of bulk anyons and deconfined topological excitations along a gapped boundary, and the condensation rules relating them. (2) As a step towards answering "why the structure of information convex looks that way and whether it has predictive power?" we look into some quantum informational constraints. The topological contribution to von Neumann entropy from each topological excitation type and certain fusion constraints are shown to emerge due to strong subadditivity, assuming fusion multiplicity is encoded in certain topological invariant manner.

I will address a long-standing problem of describing the thermodynamics of an accelerating black hole, concentrating on the special case of slowly accelerating black holes in AdS. The key
ingredient of consistent thermodynamics is to ensure that the system is not over-constrained by including the possibility of varying the string tensions that are responsible for the acceleration of the black hole. The first law assumes the standard form, with the entropy given by one quarter of the horizon area and other quantities identified by standard methods. The dual
energy-momentum tensor can be written as a three-dimensional perfect fluid plus a non-hydrodynamic contribution. Some novel thermodynamic phase behavior related to the black hole acceleration will also be discussed.

Motivated by the problem of defining the entanglement entropy of the graviton, we study the division of the phase space of general relativity across subregions. Our key requirement is demanding that the separation into subregions is imaginary---i.e., that entangling surfaces are not physical. This translates into a certain condition on the symplectic form. We find that gravitational subregions that satisfy this condition are bounded by surfaces of extremal area. We characterise the 'centre variables' of the phase space of the graviton in such subsystems, which can be taken to be the conformal class of the induced metric in the boundary, subject to a constraint involving the traceless part of the extrinsic curvature. We argue that this condition works to discard local deformations of the boundary surface to infinitesimally nearby extremal surfaces, that are otherwise available for generic codimension-2 extremal surfaces of dimension ≥ 2.

Electron-phonon interactions; Schaefer-Wolff transformation; Attractive interactions between electrons mediated by phonons; experimental evidence of superconductivity, Cooper problem. 

A self-correcting quantum memory can store and protect quantum information for a time that increases without bound with the system size, without the need for active error correction. We demonstrate that symmetry can lead to self-correction in 3D spin lattice models. In particular, we investigate codes given by 2D symmetry-enriched topological (SET) phases that appear naturally on the boundary of 3D symmetry-protected topological (SPT) phases. We find that while conventional onsite symmetries are not sufficient to allow for self-correction in commuting Hamiltonian models of this form, a generalized type of symmetry known as a 1-form symmetry is enough to guarantee self-correction. We illustrate this fact with the 3D `cluster state' model from the theory of quantum computing. This model is a self-correcting memory, where information is encoded in a 2D SET ordered phase on the boundary that is protected by the thermally stable SPT ordering of the bulk. We also investigate the gauge color code in this context. Finally, noting that a 1-form symmetry is a very strong constraint, we argue that topologically ordered systems can possess emergent 1-form symmetries, i.e., models where the symmetry appears naturally, without needing to be enforced externally. Joint work with Stephen Bartlett.

The strong interaction of quarks and gluons is described theoretically within the framework of Quantum Chromodynamics (QCD). The most promising way to evaluate QCD for all energy ranges is to formulate the theory on a 4-dimensional Euclidean space-time grid, which allows for numerical simulations on state of the art supercomputers. We will review the status of lattice QCD calculations providing examples such as the hadron spectrum and the inner structure of nucleons. We will then point to problems that cannot be solved by conventional Monte Carlo simulation techniques, i.e. non-zero baryon density, the matter-antimatter asymmetry and real time simulations. It will be demonstrated at the example of the 1+1 dimensional Schwinger model that tensor network techniques are able to overcome these problems showing that with this approach --and eventual quantum simulations-- a path for solving QCD is opening up.