Research
"Research in condensed matter physics is the art of uncovering hidden patterns in the intricate dance of atoms and electrons, allowing us to sculpt matter at the quantum level and shape the future of materials, technology, and our understanding of the fundamental nature of our universe."
Jacopo Gliozzi, Julian May-Mann, Taylor L. Hughes, Giuseppe De Tomasi arXiv:2304.12342
This work investigates the out-of-equilibrium dynamics of dipole and higher-moment conserving systems with long-range interactions, drawing inspiration from trapped ion experiments in strongly tilted potentials. We introduce a hierarchical sequence of multipole-conserving models characterized by power-law decaying couplings. Although the moments are always globally conserved, adjusting the power-law exponents of the couplings induces various regimes in which only a subset of multipole moments are effectively locally conserved. We examine the late-time hydrodynamics analytically and numerically using an effective classical framework, uncovering a rich dynamical phase diagram that includes subdiffusion, conventional diffusion, and Lévy flights. Our results are unified in an analytic reciprocal relationship that captures the nested hierarchy of hydrodynamics in multipole conserving systems where only a subset of the moments are locally conserved. Moreover, we extend our findings to higher dimensions and explore the emergence of long-time scales, reminiscent of pre-thermal regimes, in systems with low charge density. Lastly, we corroborate our results through state-of-the-art numerical simulations of a fully quantum long-range dipole-conserving system and discuss their relevance to trapped-ion experimental setups.
Distinguishing the dynamics of an Anderson insulator from a Many-Body Localized (MBL) phase is an experimentally challenging task. In this work, we propose a method based on machine learning techniques to analyze experimental snapshot data to separate the two phases. We show how to train 3D convolutional neural networks (CNNs) using space-time Fock-state snapshots, allowing us to obtain dynamic information about the system. We benchmark our method on a paradigmatic model showing MBL (t-V model with quenched disorder), where we obtain a classification accuracy of $\approx 80 %$ between an Anderson insulator and an MBL phase. We underline the importance of providing temporal information to the CNNs and we show that CNNs learn the crucial difference between an Anderson localized and an MBL phase, namely the difference in the propagation of quantum correlations. Particularly, we show that the misclassified MBL samples are characterized by an unusually slow propagation of quantum correlations, and thus the CNNs label them wrongly as Anderson localized.
Finally, we apply our method to the case with quasi-periodic potential, known as the Aubry-André model (AA model). We find that the CNNs have more difficulties in separating the two phases. We show that these difficulties are due to the fact that the MBL phase of the AA model is characterized by a slower information propagation for numerically accessible system sizes.
Florian Kotthoff, Frank Pollmann, Giuseppe De Tomasi
Phys. Rev. 104, 224307 & arXiv:2108.04244
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, Soumya Bera, Antonello Scardicchio, Ivan M. Khaymovich.
Phys. Rev. B 101, 100201 (R) (2020)
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.
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, Daniel Hetterich, Pablo Sala, and Frank Pollmann
Phys. Rev. B 100, 214313 (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.
