# Schedule

_{ This is the running order for the workshop. The three invited speakers are spread over the two days whilst the contributed talks (CT) take place on June 1st. Titles and abstracts for the invited and contributed talks can be found further down on this page. Academic institutions for all participants can be found on the participants page}

Thursday 1st June | Friday 2nd June | |||
---|---|---|---|---|

12:00-13:00 | Registration | 9:30 - 10:40 | Z. Papic | |

13:00-14:10 | V. Kravtsov | 10:40 - 11:00 | Coffee break | |

14:10-14:30 | Coffee break | 11:00 - 12:00 | Z. Papic | |

14:30-15:30 | V. Kravtsov | 12:00 - 13:00 | Lunch | |

15:40-16:05 | CT - F. Pietracaprina | 13:00 - 14:00 | Poster session 2 | |

16:05-16:30 | CT - S. Thomson | 14:00 - 15:10 | V. Dobrosavljević | |

16:30-16:45 | Coffee break | 15:10 - 15:30 | Coffee break | |

16:45-17:10 | CT - A. Smith | 15:30 - 16:30 | V. Dobrosavljević | |

17:10-17:35 | CT - E. Piatti | 16:30 - 16:45 | Concluding remarks | |

17:35-18:00 | CT - P. Barucca | |||

18:00-19:00 | Poster session 1 | |||

19:30-21:30 | Workshop dinner |

### Event locations

_{ The workshop takes place in the King’s building of the Strand campus, King’s College London. The three lectures will be held in the Nash lecture theatre (K2.31). The contributed talks, poster session and refreshments will be in room K2.40. A buffet lunch will be provided on the second day.}

### Invited speakers:

#### Professor Vladimir Kravtsov - Replica Symmetry Breaking and Non-Ergodic Extended phases on disordered Bethe lattices.

_{Introductory lecture - Multifractal distribution of the eigenfunction amplitudes: ergodic and non-ergodic extended states in single- and many-body localization
I will discuss the properties of multifractal (large-deviation) distribution of eigenfunctions coefficients of single- and many body states and its relation with other statistics of eigenfunctions and eigenvalues. In particular, I will focus at the spectrum of fractal dimensions f(\alpha) and the moments of random eigenfunctions in systems with local tree structure, such as Bethe lattice, Random Regular Graphs, Populations Dynamics network and also Rosenzweig-Porter random matrix ensemble. I will also discuss different numerical methods to characterize a multifractal state and present the results for the random regular graph and population dynamics network. Specialist talk - One step replica symmetry breaking and the fractal dimensions of wave functions on networks with local tree structure I will show how one step replica symmetry breaking formalism is capable of computing the fractal dimension D_{1} of multifractal wave functions on the Bethe lattice.}

#### Dr. Zlatko Papić - Signatures of quantum integrability in the entanglement spectrum

_{ Quantum many-body systems are challenging to study because of their exponentially large Hilbert spaces, but at the same time they represent an arena for exciting new physics which results from interactions between particles. For theoretical purposes, it is convenient to know if such systems can be expressed in a "simple" ways in terms of some nearly-free quasiparticles, or more generally if one can construct a large set of operators that approximately commute with the system’s Hamiltonian. In this talk I will discuss two ways of approaching these questions using the "entanglement spectrum". In the first part, I will show that strongly disordered systems in the many-body localized phase have a universal power-law structure in their entanglement spectra. This is a consequence of their local integrability, and distinguishes such states from typical ground states of gapped systems. In the second part, I will introduce a notion of “interaction distance” and show that the entanglement spectrum can be used to quantify “how far” an interacting ground state is from a free (Gaussian) state. I will discuss some examples of quantum spin chains and outline a few future directions. [1] M. Serbyn, A. Michailidis, D. Abanin, Z. Papic, arXiv:1605.05737. [2] C. J. Turner, K. Meichanetzidis, Z. Papic, and J. K. Pachos, arXiv:1607.02679. }

#### Professor Vladimir Dobrosavljević

_{Introductory Lecture : Effective Medium Approaches (EMA) for Disorder within DMFT
Specialist Talk : Beyond EMA - Friedel Oscillations and Electronic Griffiths Phases
Abstracts available here }

### Contributed talks:

#### Dr. Francesca Pietracaprina - Entanglement critical length at the many-body localization transition

_{ We study the details of the distribution of the entanglement spectrum (eigenvalues of the reduced density matrix) of a disordered spin chain exhibiting a many-body localization (MBL) transition. In the thermalizing region we identify the evolution under increasing system size of the eigenvalues distribution function, whose thermodynamic limit is close (but possibly different from) the Marchenko-Pastur distribution. From the analysis we extract a correlation length L_s(h) determining the minimum system size to enter the asymptotic region. We find that L_s(h) diverges at the MBL transition. We discuss the nature of the subleading corrections to the entanglement spectrum distribution and to the entanglement entropy.}

#### Dr. Steven Thomson

_{ Once thought to destroy localisation completely, we now know that adding interactions into disordered materials can lead to the formation of a many-body localised phase. This phase is characterised by an extensive number of local conserved quantities and a failure to thermalise. Consequently it cannot be described by conventional equilibrium quantum statistical mechanics, and exact numerical methods are restricted to small system sizes. Here, we present a perturbative flow equation approach: we employ a continuous unitary transform to diagonalise the prototypical XXZ spin chain Hamiltonian, show how local integrals of motion naturally emerge from this method, and go on calculate time evolution and localisation properties in the strongly-disordered regime.}

#### Adam Smith - Disorder-free Localization

_{
Localisation depends crucially on the presence of disorder -- both for the Anderson and the many-body flavours. This disorder can reside either in the parameters of the Hamiltonian or in the initial state. Here we present a model where localization arises in a simple, translationally-invariant quantum model of locally interacting spins and fermions. This system generates its own disorder dynamically giving rise to localization of the fermionic degrees of freedom and answering a decades old question: is quenched disorder a necessary condition for localization. Our model also provides a nice perspective on many-body localization and quantum disentangled liquids.}

#### Dr. Erik Piatti - Localization and scattering in ion-gated few-layer graphene: the competing roles of gate-induced disorder and ultra-high carrier density

_{ We employ ionic gating to control the electric transport properties of few-layer graphene field-effect devices up to surface carrier densities of the order of ~7x10^14 cm^-2 and down to temperatures ~3.5 K. We find that, unlike in single-layer graphene, in 3-, 4- and 5-layer graphene electric transport is dominated by electron-electron collisions below ~100 K. We also observe a logarithmic upturn of resistance below 20-30 K that we attribute to weak localization in the diffusive regime. By studying this effect as a function of carrier density and with ab-initio calculations we determine that, with the increase of gate voltage, the localization behavior is dominated by the competing effects due to the increase in both carrier density and charged scattering centers at the surface. We also tune our devices into a crossover regime between weak and strong localization, indicating that simultaneous tunability of both carrier and defect density at the surface of electric double layer gated materials is possible.
}

#### Dr. Paolo Barucca - Localization in covariance matrices of coupled heterogeneous Ornstein-Uhlenbeck processes

_{
We define a random-matrix ensemble given by the infinite-time covariance matrices of Ornstein-Uhlenbeck processes at different temperatures coupled by a Gaussian symmetric matrix. The spectral properties of this ensemble are shown to be in qualitative agreement with some stylized facts of financial markets. Through the presented model formulas are given for the analysis of heterogeneous time series. Furthermore evidence for a localization transition in eigenvectors related to small and large eigenvalues in cross-correlations analysis of this model is found, and a simple explanation of localization phenomena in financial time series is provided. Finally we identify both in our model and in real financial data an inverted-bell effect in correlation between localized components and their local temperature: high- and low-temperature components are the most localized ones. }