Polynomially filtered exact diagonalization approach to many-body localization

Polynomially filtered exact diagonalization method (POLFED) for large sparse matrices is introduced. The algorithm finds an optimal basis of a subspace spanned by eigenvectors with eigenvalues close to a specified energy target by a spectral transformation using a high order polynomial of the matrix. The memory requirements scale better with system size than in the state-of-the-art shift-invert approach. The potential of POLFED is demonstrated examining many-body localization transition in 1D interacting quantum spin-1/2 chains. We investigate the disorder strength and system size scaling of Thouless time. System size dependence of bipartite entanglement entropy and of the gap ratio highlights the importance of finite-size effects in the system. We discuss possible scenarios regarding the many-body localization transition obtaining estimates for the critical disorder strength.Comment: 4+5 pages, version accepted in Physical Review Letters, comments welcom

Toolbox for Abelian lattice gauge theories with synthetic matter

Fundamental forces of Nature are described by field theories, also known as gauge theories, based on a local gauge invariance. The simplest of them is quantum electrodynamics (QED), which is an example of an Abelian gauge theory. Such theories describe the dynamics of massless photons and their coupling to matter. However, in two spatial dimension (2D) they are known to exhibit gapped phases at low temperature. In the realm of quantum spin systems, it remains a subject of considerable debate if their low energy physics can be described by emergent gauge degrees of freedom. Here we present a class of simple two-dimensional models that admit a low energy description in terms of an Abelian gauge theory. We find rich phase diagrams for these models comprising exotic deconfined phases and gapless phases - a rare example for 2D Abelian gauge theories. The counter-intuitive presence of gapless phases in 2D results from the emergence of additional symmetry in the models. Moreover, we propose schemes to realize our model with current experiments using ultracold bosonic atoms in optical lattices.Comment: Accepted versio

Automatic Reinforcement Generation in FEM-Plate.

In this master’s thesis automatic generation of reinforcement distribution in the structural engineering program FEM-Design Plate was investigated. The reinforcement distribution proposed was to be as accurate as possible, both from a theoretical and a practical point of view. For this purpose, calculation routines considering current national codes and engineering practice have been developed. These routines are based on the results of calculations performed in FEM-Plate. The resulting reinforcement distribution shows that creating a proposal that would fully meet the requirements of an engineer is difficult to accomplish

Density dependent tunneling in the extended Bose-Hubbard model

Recently, it has become apparent that, when the interactions between polar molecules in optical lattices becomes strong, the conventional description using the extended Hubbard model has to be modified by additional terms, in particular a density-dependent tunneling term. We investigate here the influence of this term on the ground-state phase diagrams of the two dimensional extended Bose-Hubbard model. Using Quantum Monte Carlo simulations, we investigate the changes of the superfluid, supersolid, and phase-separated parameter regions in the phase diagram of the system. By studying the interplay of the density-dependent hopping with the usual on-site interaction U and nearest-neighbor repulsion V, we show that the ground-state phase diagrams differ significantly from the ones that are expected from the standard extended Bose-Hubbard model. However we find no indication of pair-superfluid behavior in this two dimensional square lattice study in contrast to the one-dimensional case

Bose-Hubbard model with random impurities: Multiband and nonlinear hopping effects

We investigate the phase diagrams of theoretical models describing bosonic atoms in a lattice in the presence of randomly localized impurities. By including multiband and nonlinear hopping effects we enrich the standard model containing only the chemical-potential disorder with the site-dependent hopping term. We compare the extension of the MI and the BG phase in both models using a combination of the local mean-field method and a Hartree-Fock-like procedure, as well as, the Gutzwiller-ansatz approach. We show analytical argument for the presence of triple points in the phase diagram of the model with chemical-potential disorder. These triple points however, cease to exists after the addition of the hopping disorder.Comment: version accepted in Phys. Rev.

Adaptive Hounsfield Scale Windowing in Computed Tomography Liver Segmentation

In computed tomography (CT) imaging, the Hounsfield Unit (HU) scale quantifies radiodensity, but its nonlinear nature across organs and lesions complicates machine learning analysis. This paper introduces an automated method for adaptive HU scale windowing in deep learning-based CT liver segmentation. We propose a new neural network layer that optimizes HU scale window parameters during training. Experiments on the Liver Tumor Segmentation Benchmark show that the learned window parameters often converge to a range encompassing clinically used windows but wider, suggesting that adjacent data may contain useful information for machine learning. This layer may enhance model efficiency with just 2 additional parameters

Stanisław Swianiewicz i jego wspomnienie o Studnickim [nota redakcyjna]

In autumn 1984 Jerzy Giedroyc published a German issue of Kultura. It contained articles by Polish authors such as Konstanty Jeleński, Adam Michnik, Zdzisław Najder, Jan Józef Lipski, Jerzy Stempowski, Czesław Miłosz, Gustaw Herling-Grudziński and Stanisław Swianiewicz. This list of renowned names emphasized the wish to familiarize the German reader with the greatest writers closely or loosely connected with the Literary Institute. The issue contained texts not only on the Polish-German relations, but was also a genuine attempt at promoting Kultura in German circles. An article by Swaniewicz was dedicated to the life of Władysław Studnicki – the most important representative of the pro-German faction during War World I and the Second Polish Republic. The article has never been published in the Polish language. Courtesy of the Literary Institute in Masoins-Laffitte, Folia Historica Cracoviensa presents the original Polish work which was later translated into German. It is a very special text. Not only does Swaniewicz perfectly outline the key tenets of Studnicki’s doctrine and detail the social backdrop of Studnicki’s opinions, but he also revisits a number of personal memories of this figure. Thanks to Swaniewicz, in addition to studying the concept of the leading Polish ‘Germanophile’, we may also sense it through the author’s insightful and, at times, surprising interpretation.Jesienią 1984 r. Jerzy Giedoryc wydał niemieckojęzyczny numer „Kultury”. Zawierał on artykuły polskich autorów takich jak m.in.: Konstanty Jeleński, Adam Michnik, Zdzisław Najder, Jan Józef Lipski, Jerzy Stempowski, Czesław Miłosz, Gustaw Herling-Grudziński oraz Stanisław Swianiewicz. Zestaw znanych nazwisk silnie podkreślał chęć przedstawienia czytelnikowi niemieckojęzycznemu  najwybitniejszych autorów mniej lub bardziej związanych z Instytutem Literackim. Prezentowane teksty nie tylko traktowały o zagadnieniu relacji polsko-niemieckich, ale też były swoistą promocją tego czym jest „Kultura” w kręgu niemieckim. Jeden z tekstów autorstwa Swianiewicza był poświęcony postaci Władysława Studnickiego – najważniejszego przedstawiciela orientacji proniemieckiej w latach I wojny światowej i II Rzeczpospolitej. Tekst nigdy nie wyszedł w języku polskim. Dzięki życzliwości Instytutu  Literackiego w Masoin Laffite na łamach pisma Folia Historica Cracoviensa ukazuje się polski pierwowzór opublikowanego niemieckiego tłumaczenia. A jest to tekst wyjątkowy. Swianiewicz nie tylko znakomicie przedstawia najważniejsze elementy doktryny Studnickiego, nie tylko wnikliwie przedstawia społeczne tło jego poglądów, ale przytacza szereg osobistych wspomnień odnośnie tej postaci. Dzięki Swianiewiczowi nie tylko poznajemy koncepcje czołowego polskiego „germanofila”, ale przede wszystkim odczujemy ją poprzez wnikliwą i miejscami zaskakująca interpretację autora

Tracking locality in time evolution of disordered systems

Using local density correlation functions for a one-dimensional spin system, we introduce a correlation function difference (CFD) which compares correlations on a given site between a full system of size $L$ and its restriction to $\ell<L$ sites. We show that CFD provides useful information on transfer of information in quantum many-body systems by considering the examples of ergodic, Anderson, and many-body localized regimes in disordered XXZ spin chain. In the ergodic phase, we find that the propagation of CFD is asymptotically faster than the spin transport but slower than the ballistic propagation implied by the Lieb-Robinson bound. In contrast, in the localized cases, we unravel an exponentially slow relaxation of CFD. Connections between CFD and other observables detecting non-local correlations in the system are discussed.Comment: 12 pages, 11 figures. Comments welcome

Slow dynamics of a mobile impurity interacting with an Anderson insulator

We investigate dynamics of a single mobile impurity immersed in a bath of Anderson localized particles and focus on the regime of relatively strong disorder and interactions. In that regime, the dynamics of the system is particularly slow, suggesting, at short times, an occurrence of many-body localization. Considering longer time scales, we show that the latter is a transient effect and that, eventually, the impurity spreads sub-diffusively and induces a gradual delocalization of the Anderson insulator. The phenomenology of the system in the considered regime of slow dynamics includes a sub-diffusive growth of mean square displacement of the impurity, power-law decay of density correlation functions of the Anderson insulator and a power-law growth of entanglement entropy in the system. We observe a similar regime of slow dynamics also when the disorder in the system is replaced by a sufficiently strong quasi-periodic potential.Comment: AAM version to be published in PR