Algebraic Many-Body Localization and its implications on information propagation

We probe the existence of a many-body localized phase (MBL-phase) in a spinless fermionic Hubbard chain with algebraically localized single-particle states, by investigating both static and dynamical properties of the system. This MBL-phase can be characterized by an extensive number of integrals of motion which develop algebraically decaying tails, unlike the case of exponentially localized single-particle states. We focus on the implications for the quantum information propagation through the system. We provide evidence that the bipartite entanglement entropy after a quantum quench has an unbounded algebraic growth in time, while the quantum Fisher information grows logarithmically

Multifractality meets entanglement: relation for non-ergodic extended states

In this work we establish a relation between entanglement entropy and fractal dimension $D$ of generic many-body wave functions, by generalizing the result of Don N. Page [Phys. Rev. Lett. 71, 1291] to the case of {\it sparse} random pure states (S-RPS). These S-RPS living in a Hilbert space of size $N$ are defined as normalized vectors with only $N^D$ ($0 \le D \le 1$) random non-zero elements. For $D=1$ these states used by Page represent ergodic states at infinite temperature. However, for $0<D<1$ the S-RPS are non-ergodic and fractal as they are confined in a vanishing ratio $N^D/N$ of the full Hilbert space. Both analytically and numerically, we show that the mean entanglement entropy ${\mathcal{S}_1}(A)$ of a subsystem $A$, with Hilbert space dimension $N_A$, scales as $\overline{\mathcal{S}_1}(A)\sim D\ln N$ for small fractal dimensions $D$, $N^D< N_A$. Remarkably, $\overline{\mathcal{S}_1}(A)$ saturates at its thermal (Page) value at infinite temperature, $\overline{\mathcal{S}_1}(A)\sim \ln N_A$ at larger $D$. Consequently, we provide an example when the entanglement entropy takes an ergodic value even though the wave function is highly non-ergodic. Finally, we generalize our results to Renyi entropies $\mathcal{S}_q(A)$ with $q>1$ and to genuine multifractal states and also show that their fluctuations have ergodic behavior in narrower vicinity of the ergodic state, $D=1$.Comment: 7 pages, 4 figures, 92 references + 9 pages, 9 figures in appendice

Solving efficiently the dynamics of many-body localized systems at strong disorder

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

Characterization of ergodicity breaking in disordered quantum systems

The interplay between quenched disorder and interaction effects opens the possibility in a closed quantum many-body system of a phase transition at finite energy density between an ergodic phase, which is governed by the laws of statistical physics, and a localized one, in which the degrees of freedom are frozen and ergodicity breaks down. The possible existence of a quantum phase transition at finite energy density is strongly questioning our understanding of the fundamental laws of nature and has generated an active field of research called many-body localization. This thesis consists of three parts and is dedicated to the understanding and characterization of the phenomenon of many-body localization, approaching it from complementary facets. In particular, borrowing methods and tools from different fields, we analyze timely problems. The first part of the thesis is devoted to detecting the many-body localization transition and to characterize both the ergodic and the localized phase it separates. Here we provide a characterization from two different perspectives: the first one is based on the study of local entanglement properties. In the second one, using tools from quantum-chaos theory, we attempt to answer the question of understanding time-irreversibility, and thus probing the breaking of ergodicity. We analyze experimentally viable observables. Moreover, we propose two different quantities to distinguish an Anderson insulating phase from a many-body localized one, which is one of the issues in experiments. The second part focuses on understanding the existence of a putative subdiffusive multifractal phase. Analyzing the quantum dynamics of the system in this region of the phase diagram, we point out the importance of finite-size effects, questioning the existence of this multifractal phase. We speculate with a possible scenario in which the diffusivity and thus ergodicity could be restored in the thermodynamic limit. Furthermore, we find that the propagation is highly non-Gaussian, which could have an important effect on understanding the critical point of the according transition. We tackle this problem also from a different angle. A possible toy-model to understand many-body localization entails the Anderson model on a random-regular graph. Also in the latter model the possible existence of an intermediate multifractal phase has been conjectured. There, studying the survival return probability of a particle with time, we give a new characterization of multifractal phases and give indication of the possible existence of this phase. Nevertheless, we also outline possible caveats. In the last part of this thesis we study the interplay between symmetry and correlated disorder in a non-interacting fermionic system. We show another possible mechanism for breaking localization. In particular, we focus on studying information and particle transport, emphasizing how the two types of propagation can be different

Quantum Mutual Information as a Probe for Many-Body Localization

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-Andr\'e-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.Comment: 4+2 pages, 5+5 figure

Persistent hyperprolactinemia and bilateral galactocele in a male infant: case report

Galactocele is a benign breast lesion, usually occurring in nursing women. This lesion is a rare cause of breast enlargement in children. In this paper we describe the case of an infant with hyperprolactinemia (which persisted throughout 15 years of clinical observation) and bilateral galactocele.We speculate that a congenital midline defect in our patient might have impaired the normal dopaminergic inhibitory tone on pituitary lactotroph cells, thus leading to an increased prolactin secretion by the pituitary gland; this, in turn, might have favored the development of the galactocele

Characterizing time-irreversibility in disordered fermionic systems by the effect of local perturbations

We study the effects of local perturbations on the dynamics of disordered fermionic systems in order to characterize time-irreversibility. We focus on three different systems, the non-interacting Anderson and Aubry-Andr\'e-Harper (AAH-) models, and the interacting spinless disordered t-V chain. First, we consider the effect on the full many-body wave-functions by measuring the Loschmidt echo (LE). We show that in the extended/ergodic phase the LE decays exponentially fast with time, while in the localized phase the decay is algebraic. We demonstrate that the exponent of the decay of the LE in the localized phase diverges proportionally to the single-particle localization length as we approach the metal-insulator transition in the AAH model. Second, we probe different phases of disordered systems by studying the time expectation value of local observables evolved with two Hamiltonians that differ by a spatially local perturbation. Remarkably, we find that many-body localized systems could lose memory of the initial state in the long-time limit, in contrast to the non-interacting localized phase where some memory is always preserved

Persistent Hyperprolactinemia and Bilateral Galactocele in a Male Infant

Galactocele is a benign breast lesion, usually occurring in nursing women. This lesion is a rare cause of breast enlargement in children. In this paper we describe the case of an infant with hyperprolactinemia (which persisted throughout 15 years of clinical observation) and bilateral galactocele. We speculate that a congenital midline defect in our patient might have impaired the normal dopaminergic inhibitory tone on pituitary lactotroph cells, thus leading to an increased prolactin secretion by the pituitary gland; this, in turn, might have favored the development of the galactocele

Non-Hermiticity induces localization: good and bad resonances in power-law random banded matrices

The power-law random banded matrix (PLRBM) is a paradigmatic ensemble to study the Anderson localization transition (AT). In $d$-dimension the PLRBM are random matrices with algebraic decaying off-diagonal elements $H_{\vec{n}\vec{m}}\sim 1/|\vec{n}-\vec{m}|^\alpha$, having AT at $\alpha=d$. In this work, we investigate the fate of the PLRBM to non-Hermiticity. We consider the case where the random on-site diagonal potential takes complex values, mimicking an open system, subject to random gain-loss terms. We provide an analytical understanding of the model by generalizing the Anderson-Levitov resonance counting technique to the non-Hermitian case. This generalization identifies two competing mechanisms due to non-Hermiticity: one favoring localization and the other delocalization. The competition between the two gives rise to AT at $d/2\le \alpha\le d$. The value of the critical $\alpha$ depends on the strength of the on-site potential, reminiscent of Hermitian disordered short-range models in $d>2$. Within the localized phase, the wave functions are algebraically localized with an exponent $\alpha$ even for $\alpha<d$. This result provides an example of non-Hermiticity-induced localization.Comment: 4.5 pages, 4 figures, 57 references + 5 pages, 4 figures in Appendice

Non-Hermitian Rosenzweig-Porter random-matrix ensemble: Obstruction to the fractal phase

We study the stability of non-ergodic but extended (NEE) phases in non-Hermitian systems. For this purpose, we generalize a so-called Rosenzweig-Porter random-matrix ensemble (RP), known to carry a NEE phase along with the Anderson localized and ergodic ones, to the non-Hermitian case. We analyze, both analytically and numerically, the spectral and multifractal properties of the non-Hermitian case. We show that the ergodic and the localized phases are stable against the non-Hermitian nature of matrix entries. However, the stability of the fractal phase depends on the choice of the diagonal elements. For purely real or imaginary diagonal potential the fractal phases is intact, while for a generic complex diagonal potential the fractal phase disappears, giving the way to a localized one.Comment: 10 pages, 6 figures, 66 reference