Probing many-body localization with neural networks

We show that a simple artificial neural network trained on entanglement spectra of individual states of a many-body quantum system can be used to determine the transition between a many-body localized and a thermalizing regime. Specifically, we study the Heisenberg spin-1/2 chain in a random external field. We employ a multilayer perceptron with a single hidden layer, which is trained on labeled entanglement spectra pertaining to the fully localized and fully thermal regimes. We then apply this network to classify spectra belonging to states in the transition region. For training, we use a cost function that contains, in addition to the usual error and regularization parts, a term that favors a confident classification of the transition region states. The resulting phase diagram is in good agreement with the one obtained by more conventional methods and can be computed for small systems. In particular, the neural network outperforms conventional methods in classifying individual eigenstates pertaining to a single disorder realization. It allows us to map out the structure of these eigenstates across the transition with spatial resolution. Furthermore, we analyze the network operation using the dreaming technique to show that the neural network correctly learns by itself the power-law structure of the entanglement spectra in the many-body localized regime.Comment: 12 pages, 10 figure

Dislocation Non-Hermitian Skin Effect

We demonstrate that crystal defects can act as a probe of intrinsic non-Hermitian topology. In particular, in point-gapped systems with periodic boundary conditions, a pair of dislocations may induce a non-Hermitian skin effect, where an extensive number of Hamiltonian eigenstates localize at only one of the two dislocations. An example of such a phase are two-dimensional systems exhibiting weak non-Hermitian topology, which are adiabatically related to a decoupled stack of Hatano-Nelson chains. Moreover, we show that strong two-dimensional point-gap topology may also result in a dislocation response, even when there is no skin effect present with open boundary conditions. For both cases, we directly relate their bulk topology to a stable dislocation non-Hermitian skin effect. Finally, and in stark contrast to the Hermitian case, we find that gapless non-Hermitian systems hosting bulk exceptional points also give rise to a well-localized dislocation response.Comment: 6 pages, 4 figures, supplement included, accepted manuscrip

Algorithms for Tensor Network Contraction Ordering

Contracting tensor networks is often computationally demanding. Well-designed contraction sequences can dramatically reduce the contraction cost. We explore the performance of simulated annealing and genetic algorithms, two common discrete optimization techniques, to this ordering problem. We benchmark their performance as well as that of the commonly-used greedy search on physically relevant tensor networks. Where computationally feasible, we also compare them with the optimal contraction sequence obtained by an exhaustive search. We find that the algorithms we consider consistently outperform a greedy search given equal computational resources, with an advantage that scales with tensor network size. We compare the obtained contraction sequences and identify signs of highly non-local optimization, with the more sophisticated algorithms sacrificing run-time early in the contraction for better overall performance.Comment: 10 pages, 10 figure

Robust Reconstruction from Chopped and Nodded Images

In ground based infrared imaging a well-known technique to reduce the influence of thermal and background noise is chopping and nodding, where four different signals of the same object are recorded from which the object is reconstructed numerically. Since noise in the data can severely affect the reconstruction, regularization algorithms have to be implemented. In this paper we propose to combine iterative reconstruction algorithms with robust statistical methods. Moreover, we study the use of multiple chopped data sets with different chopping amplitudes and the according numerical reconstruction algorithm. Numerical simulations show robustness of the proposed methods with respect to noisy data.Comment: 8 page

Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect

The classification of point gap topology in all local non-Hermitian symmetry classes has been recently established. However, many entries in the resulting periodic table have only been discussed in a formal setting and still lack a physical interpretation in terms of their bulk-boundary correspondence. Here, we derive the edge signatures of all two-dimensional phases with intrinsic point gap topology. While in one dimension point gap topology invariably leads to the non-Hermitian skin effect, non-Hermitian boundary physics is significantly richer in two dimensions. We find two broad classes of non-Hermitian edge states: (1) Infernal points, where a skin effect occurs only at a single edge momentum, while all other edge momenta are devoid of edge states. Under semi-infinite boundary conditions, the point gap thereby closes completely, but only at a single edge momentum. (2) Non-Hermitian exceptional point dispersions, where edge states persist at all edge momenta and furnish an anomalous number of symmetry-protected exceptional points. Surprisingly, the latter class of systems allows for a finite, non-extensive number of edge states with a well defined dispersion along all generic edge terminations. Instead, the point gap only closes along the real and imaginary eigenvalue axes, realizing a novel form of non-Hermitian spectral flow.Comment: 6 pages, 3 figures, 13 pages supplementary materia

Trions in Twisted Bilayer Graphene

The strong coupling phase diagram of magic angle twisted bilayer graphene (TBG) predicts a series of exact one particle charge $\pm 1$ gapped excitations on top of the integer-filled ferromagnetic ground-states. Finite-size exact diagonalization studies showed that these are the lowest charge $\pm 1$ excitations in the system (for $10$nm screening length), with the exception of charge $+1$ at filling $-1$ in the chiral limit. In the current paper we show that this "trion bound state", a $3$-particle, charge $1$ excitation of the insulating ferromagnetic ground-state of the projected Hamiltonian of TBG is the lowest charge $+1$ overall excitation at $\nu=-1$, and also for some large ($\approx 20$nm) screening lengths at $\nu=-2$ in the chiral limit and with very small binding energy. At other fillings, we show that trion bound states do exist, but only for momentum ranges that do not cover the entire moir\'e Brillouin zone. The trion bound states (at different momenta) exist for finite parameter range $w_0/w_1$ but they all disappear in the continuum far below the realistic values of $w_0/w_1= 0.8$. We find the conditions for the existence of the trion bound state, a good variational wavefunction for it, and investigate its behavior for different screening lengths, at all integer fillings, on both the electron and hole sides.Comment: 30 pages, 19 figure

Data for: A Literature Review on Methods for the Extraction of Usage Statements of Software and Data: [research data]

Software and data have become major components of modern research, which is also reflected by an increased number of software usages. Knowledge about used software and data would provide researchers a better understanding of the results of a scientific investigation and thus foster it's reproducibility. Software and data are, however, often not formally cited but their usage is mentioned in the main text. In order to assess the state of the art in extraction of such usage statements, we performed a literature review. We provide an overview of existing methods for the identification of usage statements of software and data in scientific articles. This analysis mainly focuses on technical approaches, the employed corpora, and the purpose of the investigation itself. We found four different classes of approaches that are used in the literature: 1.) term search, 2.) manual extraction, 3.) rule-based extraction, and 4.) extraction based on supervised learning

Automatic Behavior Assessment from Uncontrolled Everyday Audio Recordings by Deep Learning

The manual categorization of behavior from sensory observation data to facilitate further analyses is a very expensive process. To overcome the inherent subjectivity of this process, typically, multiple domain experts are involved, resulting in increased efforts for the labeling. In this work, we investigate whether social behavior and environments can automatically be coded based on uncontrolled everyday audio recordings by applying deep learning. Recordings of daily living were obtained from healthy young and older adults at randomly selected times during the day by using a wearable device, resulting in a dataset of uncontrolled everyday audio recordings. For classification, a transfer learning approach based on a publicly available pretrained neural network and subsequent fine-tuning was implemented. The results suggest that certain aspects of social behavior and environments can be automatically classified. The ambient noise of uncontrolled audio recordings, however, poses a hard challenge for automatic behavior assessment, in particular, when coupled with data sparsity