## Research

Oliver Hart, Giuseppe De Tomasi, Claudio Castelnovo**Phys. Rev. Research 2, 043267 (2020)**** ****(Editors' Suggestion)**

In this work we investigate the effects of configurational disorder on the eigenstates and dynamical properties of a tight-binding model on a quasi-one-dimensional comb lattice, consisting of a backbone decorated with linear offshoots of randomly distributed lengths. We show that all eigenstates are exponentially localized along the backbone of the comb. Moreover, we demonstrate the presence of an extensive number of compact localized states with precisely zero localization length. We provide an analytical understanding of these states and show that they survive in the presence of density-density interactions along the backbone of the system where, for sufficiently low but finite particle densities, they form many-body scar states. Finally, we discuss the implications of these compact localized states on the dynamical properties of systems with configurational disorder, and the corresponding appearance of long-lived transient behaviour in the time evolution of physically relevant product states.

Giuseppe De Tomasi, Ivan M. Khaymovich**Phys. Rev. Lett. 124, 200602 (2020)**

In this work, we built up a bridge between ergodic properties extracted form entanglement measurements and the ones from multifractal analysis. We generalised the work of Don. N. Page [Phys. Rev. Lett. 71, 1291] for the entanglement entropy, to the case of non-ergodic but extended (NEE) states. In particular, by implementing the NEE states with a new and simple class of random states, which live in a fractal of the Fock space, we compute, both analytically and numerically, its von Neumann/Renyi entropy. Remarkably, we show that the entanglement, both Renyi and von Neumann, entropy can still show a fully ergodic behaviour, even tough the wave function lives in a vanishing ratio of the full Hilbert space in the thermodynamic limit.

Giuseppe De Tomasi, Daniel Hetterich, Pablo Sala, and Frank Pollmann**Phys. Rev. B 100, 214313 (2019)**

We study the t−V disordered spinless fermionic chain in the strong coupling regime, t/V→0. Strong interactions highly hinder the dynamics of the model, fragmenting its Hilbert space into exponentially many blocks in system size. Macroscopically, these blocks can be characterized by the number of new degrees of freedom, which we refer to as movers. We focus on two limiting cases: Blocks with only one mover and the ones with a finite density of movers. The former many-particle block can be exactly mapped to a single-particle Anderson model with correlated disorder in one dimension. As a result, these eigenstates are always localized for any finite amount of disorder. The blocks with a finite density of movers, on the other side, show an MBL transition that is tuned by the disorder strength. Moreover, we provide numerical evidence that its ergodic phase is diffusive at weak disorder. Approaching the MBL transition, we observe sub-diffusive dynamics at finite time scales and find indications that this might be only a transient behavior before crossing over to diffusion.

Giuseppe De Tomasi, Soumya Bera, Antonello Scardicchio, Ivan M. Khaymovich.**Phys. Rev. B 101, 100201 (R) (2020)**

We study the finite-time dynamics of an initially localized wave-packet in the Anderson model on the random regular graph (RRG). Considering the full probability distribution of a particle to be at some distance x from the initial state at time t, we give evidence that dynamics is sub-diffusively over a range of disorder strengths, wider than a putative non-ergodic phase. We provide a detailed analysis of the propagation in space-time (x,t) domain, identifying four different regimes. These regimes in (x,t) are determined by the position of a wave-front, which moves sub-diffusively to the most distant sites. We support our numerical results by a self-consistent semi-classical picture of wavepacket. Importantly, the Anderson model on the RRG can be considered as proxy of the many-body localization transition (MBL) on the Fock space of a generic interacting system. In the final discussion, we outline possible implications of our findings for MBL.

Giuseppe De Tomasi, Frank Pollmann, and Markus Heyl.**Phys. Rev. B 99, 241114 (R) (2019)**

We introduce a method to efficiently study the dynamical properties of many-body localized systems in the regime of strong disorder and weak interactions. Our method reproduces qualitatively and quantitatively the real-time evolution with a polynomial effort in system size and independent of the desired time scales. We use our method to study quantum information propagation, correlation functions, and temporal fluctuations in one- and two-dimensional MBL systems. Moreover, we outline strategies for a further systematic improvement of the accuracy and we point out relations of our method to recent attempts to simulate the real-time dynamics of quantum many-body systems in classical or artificial neural networks.

Giuseppe De Tomasi, Soumya Bera, Jens H. Bardarson, Frank Pollmann.**Phys. Rev. Lett. 118, 016804 (2017)**

We demonstrate that the quantum mutual information (QMI) is a useful probe to study many-body localization (MBL). First, we focus on the detection of a metal--insulator transition for two different models, the noninteracting Aubry-André-Harper model and the spinless fermionic disordered Hubbard chain. We find that the QMI in the localized phase decays exponentially with the distance between the regions traced out, allowing us to define a correlation length, which converges to the localization length in the case of one particle. Second, we show how the QMI can be used as a dynamical indicator to distinguish an Anderson insulator phase from an MBL phase. By studying the spread of the QMI after a global quench from a random product state, we show that the QMI does not spread in the Anderson insulator phase but grows logarithmically in time in the MBL phase.