10:00 – 18:00, lecture hall **P.04**,** **Jadranska 21.

**Programme:**

9:30 |
coffee and discussions |

**10:15 ** |
**Márton Mestyán **(SISSA): *Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics* |

10:50 |
**Lev Vidmar ****(IJS Ljubljana): ** *Quantum chaos challenges many-body localization* |

12:25 |
**Tiago Mendes-Santos** (ICTP):* Entanglement guided search for parent Hamiltonians* |

12:00 |
lunch |

13:00 |
discussions |

15:15 |
**Spyros Sotiriadis** (FMF **Ljubljana): ***Quantum dynamics in the sine-Gordon model* |

15:50 |
**Jacopo Sisti** **(SISSA): ***Entanglement entropy in higher dimensional CFTs and holography* |

16:25 |
**Giuliano Giudici** (ICTP): *Measuring von Neumann entanglement entropies without wave functions* |

17:00 |
conclusion |

**Márton Mestyán:** *Molecular dynamics simulation of entanglement spreading in generalized hydrodynamics (arXiv:1905.03206)*

The so-called flea gas is an elementary yet very powerful method that allows the simulation of the out-of-equilibrium dynamics after quantum quenches in integrable systems. We show that, after supplementing it with minimal information about the initial state correlations, the flea gas provides a versatile tool to simulate the dynamics of entanglement-related quantities. The method can be applied to any quantum integrable system and to a large class of initial states. Moreover, the efficiency of the method does not depend on the choice of the subsystem configuration. We implement the flea gas dynamics for the gapped anisotropic Heisenberg XXZ chain, considering quenches from globally homogeneous and piecewise homogeneous initial states. We compute the time evolution of the entanglement entropy and the mutual information in these quenches, providing strong confirmation of recent analytical results obtained using the Generalized Hydrodynamics approach. The method also allows us to obtain the full-time dynamics of the mutual information after quenches from inhomogeneous settings, for which no analytical results are available.

**Lev Vidmar:** *Quantum chaos challenges many-body localization (arXiv:1905.06345)*

Characterizing states of matter through the lens of their ergodic properties is a fascinating new direction of research. In the quantum realm, the many-body localization (MBL) was proposed to be the paradigmatic nonergodic phenomenon, which extends the concept of Anderson localization to interacting systems. At the same time, random matrix theory has established a powerful framework for characterizing the onset of quantum chaos and ergodicity (or the absence thereof) in quantum many-body systems. Here we study a paradigmatic class of models that are expected to exhibit MBL, i.e., disordered spin chains with Heisenberg-like interactions. Surprisingly, we observe that exact calculations show no evidence of approaching MBL while increasing disordered strength in the ergodic regime. Moreover, a scaling analysis suggests that quantum chaotic properties survive for any disorder strength in the thermodynamic limit. Our results are based on calculations of the spectral form factor, which provides a powerful measure for the emergence of many-body quantum chaos.

**Tiago Mendes-Santos:** *Entanglement guided search for parent Hamiltonians*

We introduce a method for the search of parent Hamiltonians of input wave-functions based on the structure of their reduced density matrix. The two key elements of our recipe are an ansatz on the relation between reduced density matrix and parent Hamiltonian that is exact at the field theory level, and a minimization procedure on the space of relative entropies, which is particularly convenient due to its convexity. As examples, we show how our method correctly reconstructs the parent Hamiltonian correspondent to several non-trivial ground state wave functions, including conformal and symmetry-protected-topological phases, and quantum critical points of two-dimensional antiferromagnets described by strongly coupled field theories. Our results show the entanglement structure of ground state wave-functions considerably simplifies the search for parent Hamiltonians.

**Spyros Sotiriadis:** *Quantum dynamics in the sine-Gordon model*

The study of dynamics in quantum many-body systems is one of the main challenges of modern theoretical physics. While a large amount of intuition has been drawn from weakly interacting systems, linear response theory or semiclassical approximations, the dynamics of strongly interacting systems far from equilibrium remains largely unexplored. We study the dynamics of an interacting Quantum Field Theory, the sine-Gordon model, after an abrupt change of the parameters, a protocol known as “Quantum Quench”. Our focus is on the time evolution of correlation functions, which we study using a combination of numerical and analytical techniques.

**Jacopo Sisti: ***Entanglement entropy in higher dimensional CFTs and holography*

Entanglement entropy is a quantity of great interest in diverse fields of physics like condensed matter, statistical and high energy physics. In this talk, I will review some aspects of entanglement entropy in higher dimensional quantum field theories mainly focusing on CFTs that admit a holographic dual. In such theories, the Ryu–Takayanagi formula identifies the entanglement entropy of a spatial region with the area of the minimal hypersurface anchored to the entangling surface and that extends along the holographic direction of the space-time. The holographic duality is a useful tool also to study CFTs with boundary. In particular, I will show some analytical and numerical results on minimal surfaces in space-times dual to (2+1)-dimensional BCFTs.

**Giuliano Giudici: ***Measuring von Neumann entanglement entropies without wave functions*

It is nowadays a well known fact that the von Neumann entropy (VNE) of the ground state is a powerful tool to characterize many-body quantum systems, since it provides distinctive information such as length of correlations and universal data of critical systems. Despite its central role as a diagnostic tool for low-energy properties of many-body Hamiltonians, its measurement has so far been elusive both from an experimental and — beyond one dimension — numerical point of view. Here we propose a method to compute the ground state VNE without accessing the many-body wave function. The method is based on the knowledge, from quantum field theory, of the entanglement Hamiltonian of the ground state. We benchmark our technique on critical quantum spin chains, and apply it to several two-dimensional quantum magnets, where we are able to unambiguously determine the onset of area law, together with logarithmic corrections independent of the geometry of the bipartition. We finally focus on one-dimensional critical systems whose large distance behaviour is conformally invariant. We investigate to which extent it is possible to extract the central charge by computing the entanglement capacity, which is simply related to the expectation value of the energy density and thus easily accessible in experiments.