4,670 research outputs found
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 (NH) 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 NH skin effect, NH 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) NH 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. Concomitantly, the point gap only closes along the real and imaginary eigenvalue axes, realizing a novel form of NH spectral flow
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 gapped excitations
on top of the integer-filled ferromagnetic ground-states. Finite-size exact
diagonalization studies showed that these are the lowest charge
excitations in the system (for nm screening length), with the exception of
charge at filling in the chiral limit. In the current paper we show
that this "trion bound state", a -particle, charge excitation of the
insulating ferromagnetic ground-state of the projected Hamiltonian of TBG is
the lowest charge overall excitation at , and also for some large
(nm) screening lengths at 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 but they all disappear in the continuum far below the
realistic values of . 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
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