Discrete disorder models for many-body localization

Using exact diagonalization technique, we investigate the many-body localization phenomenon in the 1D Heisenberg chain comparing several disorder models. In particular we consider a family of discrete distributions of disorder strengths and compare the results with the standard uniform distribution. Both statistical properties of energy levels and the long time non-ergodic behavior are discussed. The results for different discrete distributions are essentially identical to those obtained for the continuous distribution, provided the disorder strength is rescaled by the standard deviation of the random distribution. Only for the binary distribution significant deviations are observed.Comment: version accepted in Phys. Rev.

Many-body quantum boomerang effect

We study numerically the impact of many-body interactions on the quantum boomerang effect. We consider various cases: weakly interacting bosons, the Tonks-Girardeau gas, and strongly interacting bosons (which may be mapped onto weakly interacting fermions). Numerical simulations are performed using the time-evolving block decimation algorithm, a quasi-exact method based on matrix product states. In the case of weakly interacting bosons, we find a partial destruction of the quantum boomerang effect, in agreement with the earlier mean-field study [Phys. Rev. A \textbf{102}, 013303 (2020)]. For the Tonks-Girardeau gas, we show the presence of the full quantum boomerang effect. For strongly interacting bosons, we observe a partial boomerang effect. We show that the destruction of the quantum boomerang effect is universal and does not depend on the details of the interaction between particles.Comment: comments welcome of course!

Quantum boomerang effect for interacting particles

When a quantum particle is launched with a finite velocity in a disordered potential, it may surprisingly come back to its initial position at long times and remain there forever. This phenomenon, dubbed ``quantum boomerang effect'', was introduced in [Phys. Rev. A 99, 023629 (2019)]. Interactions between particles, treated within the mean-field approximation, are shown to partially destroy the boomerang effect: the center of mass of the wave packet makes a U-turn, but does not completely come back to its initial position. We show that this phenomenon can be quantitatively interpreted using a single parameter, the average interaction energy.Comment: 7 + 2 pages, 9 + 2 figures, added discussion about strong disorder case in Conclusio

Berezinskii approach to disordered spin systems with asymmetric scattering and application to the quantum boomerang effect

We extend the Berezinskii diagrammatic technique to one-dimensional disordered spin systems, in which time-reversal invariance is broken due to a spin-orbit coupling term inducing left-right asymmetric scattering. We then use this formalism to theoretically describe the dynamics of the quantum boomerang effect, a recently discovered manifestation of Anderson localization. The theoretical results are confirmed by exact numerical simulations of wave-packet dynamics in a random potential

Investigating structural and functional aspects of the brain’s criticality in stroke

This paper addresses the question of the brain’s critical dynamics after an injury such as a stroke. It is hypothesized that the healthy brain operates near a phase transition (critical point), which provides optimal conditions for information transmission and responses to inputs. If structural damage could cause the critical point to disappear and thus make self-organized criticality unachievable, it would offer the theoretical explanation for the post-stroke impairment of brain function. In our contribution, however, we demonstrate using network models of the brain, that the dynamics remain critical even after a stroke. In cases where the average size of the second-largest cluster of active nodes, which is one of the commonly used indicators of criticality, shows an anomalous behavior, it results from the loss of integrity of the network, quantifiable within graph theory, and not from genuine non-critical dynamics. We propose a new simple model of an artificial stroke that explains this anomaly. The proposed interpretation of the results is confirmed by an analysis of real connectomes acquired from post-stroke patients and a control group. The results presented refer to neurobiological data; however, the conclusions reached apply to a broad class of complex systems that admit a critical state

Effet boomerang quantique dans les gaz atomiques désordonnés ultra-froids

Nous étudions théoriquement et numériquement l'effet boomerang quantique - c'est-à-dire le retour à son point de départ d'un paquet d'ondes lancé avec une vitesse non nulle - dans les gaz atomiques désordonnés ultra-froids. Nous étudions tout d'abord l'effet d'une rupture de la symétrie par renversement du temps et montrons que, contrairement à ce qui était couramment admis, cette symétrie n'est pas une condition nécessaire à la présence de l'effet boomerang. Ensuite, nous étudions l'impact des interactions sur l'effet boomerang, en utilisant l'approximation de champ moyen. Dans le cadre de l'équation de Gross-Pitaevskii, nous montrons que les interactions conduisent à une destruction partielle de l'effet et identifions un paramètre universel qui décrit cette destruction. Enfin, nous étudions numériquement l'effet des interactions en utilisant une approche "many-body" quasi-exacte. À cette fin, nous étudions les bosons en interaction faible, le gaz de Tonks-Girardeau, et les bosons en interaction forte, qui correspondent à des fermions en interaction faible. Nous observons que les bosons faiblement interagissant présentent une destruction plus forte de l'effet boomerang que dans le cadre du champ moyen, ce qui signifie que les fluctuations quantiques jouent un rôle majeur. Pour le gaz de Tonks-Girardeau, nous montrons montrent que le phénomène de boomerang quantique est complet. Les bosons en forte interaction, où l'effet boomerang n'est que partiel, fournissent la preuve que la destruction de l'effet ne dépend pas des détails des interactions entre particules.In this thesis, we theoretically and numerically investigate the quantum boomerang effect - i.e. the return of a wave packet launched with a nonzero velocity to its initial position - in ultra-cold disordered atomic gases. We address three main problems. We study the effect of the time-reversal symmetry breaking on the existence of the quantum boomerang phenomenon. We show that time-reversal symmetry is not a necessary condition for the presence of the quantum boomerang. Next, we investigate the impact of interactions on the quantum boomerang effect, using the mean-field approximation. The interactions lead to partial destruction of the boomerang effect. Within the framework of the Gross-Pitaevskii equation, we identify a universal parameter that describes the observed destruction of the particle's return to the origin. Finally, we numerically study the effect of interactions using a quasi-exact approach. To this end, we study weakly interacting bosons, the Tonks-Girardeau gas, and strongly interacting bosons, which map to weakly interacting fermions. We find that weakly interacting bosons exhibit stronger destruction of the boomerang effect than in the case of the mean-field approach, thus that quantum fluctuations play a major role. Results for the Tonks-Girardeau gas show the existence of the full quantum boomerang phenomenon. Moreover, the results for strongly interacting bosons, where the boomerang is also only partial, provide evidence that the destruction of the quantum boomerang effect does not depend on the details of the interactions between particles

Many-body localization in spin systems

Przedmiotem pracy było zbadanie wpływu różnych modeli nieporządku na zjawisko lokalizacji wielociałowej w jednowymiarowym modelu Heisenberga. Wśród badanych nieporządków znajdowały się rozkłady dyskretne, a także rozkład ciągły. Pierwszą część pracy stanowią obliczenia pozwalające na badanie przejścia pomiędzy fazami zlokalizowaną i zdelokalizowaną wykorzystujące statystyczne własności Hamiltonianów. W przeprowadzonej analizie wykazano zbieżność wyników modeli dyskretnych (od potrójnego wzwyż) z modelem ciągłym. Drugim przebadanym aspektem była ewolucja czasowa parametru porządku, pozwalającego na stwierdzenie lokalizacji. Wykonana analiza pokazała, że poszczególne modele różnią się, choć posiadają wspólne cechy. Obliczenia analityczne potwierdziły te rezultaty, a także wskazały, że w wyniku lokalizacji poszczególne spiny w układzie oddziałują jedynie z najbliższymi sąsiadami.In this thesis an influence of various disorder models on the many-body localization phenomena was investigated. The calculations were performed for 1 dimensional Heisenberg model. Both discrete and continuous distributions were considered. The first part of this thesis presents computations that allowed for study of transition between localized and delocalized phases, using statistical properties of Hamiltonians. The analysis carried out showed compatibility of results from discrete models (from ternary upward) with the continuous one. In the second part, the time evolution of order parameter was studied. Its dynamics allowed for confirmation of localization. Calculations showed that models differ from each other, though have some similarities. Analytical approach confirmed these results and pointed out also that due to localization, spins in the system interact only with the nearest neighbors

Entanglement in multipartite systems

W pracy omówiliśmy podstawy splątania kwantowego w układach dwu- oraz wielocząstkowych. Zaprezentowaliśmy dwie metody graficzne służące do analizowania splątania w układach kwantowych. Reprezentacja grafowa opiera się na konstruowaniu stanów kwantowych na podstawie nieskierowanych grafów prostych, w których krawędzie można utożsamiać z nielokalnym oddziaływaniem pomiędzy cząstkami. Reprezentacja piktograficzna służy graficznemu przedstawianiu stanów wielocząstkowych. Dzięki swojej konstrukcji umożliwia badanie właściwości stanów poprzez analizę symetrii występującej na piktogramach i samopodobieństwu. Łącząc obie reprezentacje znaleźliśmy trzy klasy stanów grafowych, których piktogramy są samopodobne, a także posiadają pewne symetrie. Są to grafy liniowe, cykle oraz grafy pełne zdefiniowane dla dowolnej liczby cząstek. Dodatkowo zaproponowaliśmy ograniczenia na entropię splątania wyżej wymienionych stanów grafowych.In this paper, we discussed the basics of quantum entanglement in bi- and multipartite systems. We presented two graphical methods to analyze entanglement in quantum systems. Graph representation is based on the construction of quantum states using simple graphs, where the edges can be identified with the nonlocal interactions between particles. Pictographic representation is a graphical presentation of multipartite states. Due to its design, it enables the study of the properties of states through the analysis of symmetries occurring on pictograms and self-similarity. Combining both representations we found three classes of graph states that pictograms are self-similar, and also have some symmetries. These are linear graphs, cycle graphs and complete graphs, defined for any number of particles. In addition, we proposed constrains on the entropy of entanglement of aforementioned graph states

Quantum boomerang effect in systems without time-reversal symmetry

International audienceIn an Anderson localized system, a quantum particle with a nonzero initial velocity returns, on average, to its origin. This recently discovered behavior is known as the quantum boomerang effect. Time-reversal invariance was initially thought to be a necessary condition for the existence of this phenomenon. We theoretically analyze the impact of the symmetry breaking on the phenomenon using a one-dimensional system with a spin-orbit coupling and show that the time-reversal invariance is not necessary for the boomerang effect to occur. We explain this behavior giving sufficient symmetry conditions for the boomerang effect to occur when time-reversal symmetry is broken