Learning impurity spectral functions from density of states

Using numerical renormalization group calculation, we construct a dataset with 100 K samples, and train six different neural networks for the prediction of spectral functions from density of states (DOS) of the host material. We find that a combination of gated recurrent unit (GRU) network and bidirectional GRU (BiGRU) performances the best among all the six neural networks. The mean absolute error of the GRU + BiGRU network can reach 0.052 and 0.043 when this network is evaluated on the original dataset and two other independent datasets. The average time of spectral function predictions from machine learning is on the scale of 10^-5-10^-6that of traditional impurity solvers for Anderson impurity model. This investigation pave the way for the application of recurrent neural network and convolutional neural network in the prediction of spectral functions from DOSs in machine learning solvers of magnetic impurity problems.

Visualizing pairing symmetry in nematic superconductors using spin-polarized spectroscopy of magnetic impurities

We study the spin-polarized spectral properties of Yu-Shiba-Rusinov resonance states induced by magnetic impurities in 2- and 3-dimensional nematic superconductors: few layer Bi₂Te₃ grown on FeTe_0.55Se_0.45 (2D) and Cu _x Bi₂Se₃ (3D). We focus on the relationship between pairing symmetry and the spatial structure of spin-polarized spectroscopy. We calculate the spin-polarized local density of states (SP LDOS) and the corresponding Fourier transformation using the T-matrix method for both the 2- and 3-dimensional materials. Various situations with different impurity orientations and different SP LDOSs have been investigated. We find that, like the quasiparticle interference spectrum, the spin-polarized spectroscopy can be applied to distinguish threefold rotation symmetric pairings, e.g. the plain s-wave pairing, chiral p -wave pairing, etc, and nematic pairings in these materials.

Magnetic impurity resonance states for different pairing symmetries in twisted bilayer graphene

In this work, we study the magnetic impurity resonance states in the superconducting phase of 'magic' angle twisted bilayer graphene for different pairing symmetries. Using a two-orbital model on the emergent honeycomb lattice, we find that the resonance states are dramatically different for [Formula: see text]-wave pairing and topological nontrivial pairings. When the magnetic impurity is located at one site of the emergent honeycomb lattice, i.e. the center of the AB spot of the moiré pattern, the spacial distributions of the resonance states will break both the threefold and twofold rotation symmetries of [Formula: see text] point group for pairing symmetries which belong to the irreducible representations of this point group. When the magnetic impurity is located at the center of the emergent honeycomb lattice i.e. the center of the AA spot of the moiré pattern, the appearance of resonance peak at the position close to the impurity can be considered as a strong evidence of non-[Formula: see text]-wave pairing.

Resonance states near a quantum magnetic impurity in single-layer FeSe superconductors with d-wave symmetry

In this work, we investigate the local density of states (LDOS) near a magnetic impurity in single-layer FeSe superconductors. The two-orbital model with spin-orbit coupling proposed in Agterberg et al (2017 Phys. Rev. Lett. 119 267001) is used to describe the FeSe superconductor. In the strong coupling regime, two impurity resonance peaks appear with opposite resonance energies in the LDOS spectral function. For strong spin-orbit coupling, the superconducting gap in this model is d-wave symmetric with nodes, the spatial distributions of the LDOS at the two resonance energies are fourfold symmetric, which reveals typical characteristic of d-wave pairing. When the spin-orbit coupling is not strong enough to close the superconducting gap, we find that the spatial distribution of the LDOS at one of the resonance energies manifests s-wave symmetry, while the pairing potential preserves d-wave symmetry. This result is consistent with previous experimental investigations.

Thermodynamics of two-impurity Anderson model with Dzyaloshinskii-Moriya interaction

In this work, we use the numerical renormalization group (NRG) theory to study the thermodynamics of the two-impurity Anderson model. Two different methods are used to estimate the effect of Dzyaloshiskii-Moriya (DM) interaction on the variation of the Kondo temperature. When the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction is vanishing, the two different estimations give different tendencies. If we use the peak of the specific heat to identify the variation of the Kondo temperature versus the DM interaction, we get an almost linear function. However, if we use the low temperature universal curve of the impurity entropy, we get a quadratic function. These results indicate that previous debates about the influence of spin-orbit coupling on the Kondo temperature may come from the different definitions of the Kondo temperature. When the RKKY interaction is ferromagnetic, there are two stages of Kondo screening. Both estimations demonstrate that the second stage of the Kondo temperature is exponentially dependent on the DM interaction. There results are dramatically different from those calculated via perturbation theory.

Guided simulated annealing method for optimization problems

Incorporating the concept of order parameter of the mean-field theory into the simulated annealing method, we present an optimization algorithm, the guided simulated annealing method. In this method mean-field order parameters are calculated to guide the configuration search for the global minimum. Allowing fluctuations and improvement of mean-field values iteratively, this method successfully identifies global minima for several difficult optimization problems. Application of this method to the HP lattice-protein model has found another lowest-energy state for an N=100 sequence that was not found by other methods before. Results for spin glass models are also presented which show improvement over the previous results.