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Hans Gerd Evertz - One of the best experts on this subject based on the ideXlab platform.
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dynamical mean field theory of the anderson hubbard model with local and nonlocal disorder in tensor formulation
Physical Review B, 2021Co-Authors: Andreas Weh, Y Zhang, Andreas Ostlin, Hanna Terletska, D Bauernfeind, Kaming Tam, Hans Gerd Evertz, Krzysztof Byczuk, D Vollhardt, L ChioncelAbstract:To explore correlated electrons in the presence of local and nonlocal disorder, the Blackman-Esterling-Berk method for averaging over off-diagonal disorder is implemented into dynamical mean-field theory using tensor notation. The impurity model combining disorder and correlations is solved using the recently developed fork tensor-product state solver, which allows one to calculate the single particle spectral functions on the real-Frequency Axis. In the absence of off-diagonal hopping, we establish exact bounds of the spectral function of the noninteracting Bethe lattice with coordination number $Z$. In the presence of interaction, the Mott insulating paramagnetic phase of the one-band Hubbard model is computed at zero temperature in alloys with site- and off-diagonal disorder. When the Hubbard $U$ parameter is increased, transitions from an alloy band insulator through a correlated metal into a Mott insulating phase are found to take place.
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dynamical mean field theory on the real Frequency Axis p d hybridization and atomic physics in srmno3
Physical Review B, 2018Co-Authors: D Bauernfeind, Robert Triebl, Manuel Zingl, Markus Aichhorn, Hans Gerd EvertzAbstract:We investigate the electronic structure of SrMnO$_3$ with Density Functional Theory (DFT) plus Dynamical Mean-Field Theory (DMFT). Within this scheme the selection of the correlated subspace and the construction of the corresponding Wannier functions is a crucial step. Due to the crystal field splitting of the Mn-$3d$ orbitals and their separation from the O-2$p$ bands, SrMnO$_3$ is a material where on first sight a 3-band $d$-only model should be sufficient. However, in the present work we demonstrate that the resulting spectrum is considerably influenced by the number of correlated orbitals and the number of bands included in the Wannier function construction. For example, in a $d$-$dp$ model we observe a splitting of the \tg lower Hubbard band into a more complex spectral structure, not observable in $d$-only models. To illustrate these high-Frequency differences we employ the recently developed Fork Tensor Product State (FTPS) impurity solver, as it provides the necessary spectral resolution on the real-Frequency Axis. We find that the spectral structure of a 5-band $d$-$dp$ model is in good agreement with PES and XAS experiments. Our results demonstrate that the FTPS solver is capable of performing full 5-band DMFT calculations directly on the real-Frequency Axis.
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dynamical mean field theory on the real Frequency Axis p d hybridization and atomic physics in srmno 3
Physical Review B, 2018Co-Authors: D Bauernfeind, Hans Gerd Evertz, Robert Triebl, Manuel Zingl, Markus AichhornAbstract:We investigate the electronic structure of ${\mathrm{SrMnO}}_{3}$ with density functional theory plus dynamical mean-field theory (DMFT). Within this scheme the selection of the correlated subspace and the construction of the corresponding Wannier functions is a crucial step. Due to the crystal-field splitting of the Mn-$3d$ orbitals and their separation from the $\mathrm{O}\text{\ensuremath{-}}2p$ bands, ${\mathrm{SrMnO}}_{3}$ is a material where on first sight a three-band $d$-only model should be sufficient. However, in the present work we demonstrate that the resulting spectrum is considerably influenced by the number of correlated orbitals and the number of bands included in the Wannier function construction. For example, in a $d\text{\ensuremath{-}}dp$ model we observe a splitting of the ${t}_{2g}$ lower Hubbard band into a more complex spectral structure, not observable in $d$-only models. To illustrate these high-Frequency differences we employ the recently developed fork tensor product state (FTPS) impurity solver, as it provides the necessary spectral resolution on the real-Frequency Axis. We find that the spectral structure of a five-band $d\text{\ensuremath{-}}dp$ model is in good agreement with PES and XAS experiments. Our results demonstrate that the FTPS solver is capable of performing full five-band DMFT calculations directly on the real-Frequency Axis.
Ming Liang - One of the best experts on this subject based on the ideXlab platform.
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a generalized synchrosqueezing transform for enhancing signal time Frequency representation
Signal Processing, 2012Co-Authors: Chuan Li, Ming LiangAbstract:High-quality time-Frequency representation (TFR) is important for reliable signal analysis. The diffusions of the TFR energy along time and/or Frequency axes lead to ambiguous TFR and hence misleading signal analysis results. Synchrosqueezing is an adaptive and invertible transform developed to improve the quality or readability of the wavelet-based TFR by condensing it along the Frequency Axis. However, the original synchrosqueezing method could be handicapped by time-dimension diffusions of the wavelet coefficients. As such, we propose a generalized synchrosqueezing transform (GST) approach to deal with the diffusions in both time and Frequency dimensions. For the signal with a constant Frequency, we have shown that the wavelet diffusion only occurs at Frequency dimension. Based on this observation, the original signal with time-varying instantaneous Frequency is mapped to another analytical signal with constant Frequency to facilitate the synchrosqueezing. A time-scale domain restoration operation is then presented to obtain a TFR with concentrated wavelet ridge. The performance of the proposed GST for signal TFR enhancement has been demonstrated by our simulation study.
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an adaptive sk technique and its application for fault detection of rolling element bearings
Mechanical Systems and Signal Processing, 2011Co-Authors: Yanxue Wang, Ming LiangAbstract:In this paper, we propose an adaptive spectral kurtosis (SK) technique for the fault detection of rolling element bearings. The primary contribution is adaptive determination of the bandwidth and center Frequency. This is implemented with successive attempts to right-expand a given window along the Frequency Axis by merging it with its subsequent neighboring windows. Influence of the parameters such as the initial window function, bandwidth and window overlap on the merged windows as well as how to choose those parameters in practical applications are explored. Based on simulated experiments, it can be found that the proposed technique can further enhance the SK-based method as compared to the kurtogram approach. The effectiveness of the proposed method in fault detection of the rolling element bearings is validated using experimental signals.
D Bauernfeind - One of the best experts on this subject based on the ideXlab platform.
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dynamical mean field theory of the anderson hubbard model with local and nonlocal disorder in tensor formulation
Physical Review B, 2021Co-Authors: Andreas Weh, Y Zhang, Andreas Ostlin, Hanna Terletska, D Bauernfeind, Kaming Tam, Hans Gerd Evertz, Krzysztof Byczuk, D Vollhardt, L ChioncelAbstract:To explore correlated electrons in the presence of local and nonlocal disorder, the Blackman-Esterling-Berk method for averaging over off-diagonal disorder is implemented into dynamical mean-field theory using tensor notation. The impurity model combining disorder and correlations is solved using the recently developed fork tensor-product state solver, which allows one to calculate the single particle spectral functions on the real-Frequency Axis. In the absence of off-diagonal hopping, we establish exact bounds of the spectral function of the noninteracting Bethe lattice with coordination number $Z$. In the presence of interaction, the Mott insulating paramagnetic phase of the one-band Hubbard model is computed at zero temperature in alloys with site- and off-diagonal disorder. When the Hubbard $U$ parameter is increased, transitions from an alloy band insulator through a correlated metal into a Mott insulating phase are found to take place.
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dynamical mean field theory on the real Frequency Axis p d hybridization and atomic physics in srmno3
Physical Review B, 2018Co-Authors: D Bauernfeind, Robert Triebl, Manuel Zingl, Markus Aichhorn, Hans Gerd EvertzAbstract:We investigate the electronic structure of SrMnO$_3$ with Density Functional Theory (DFT) plus Dynamical Mean-Field Theory (DMFT). Within this scheme the selection of the correlated subspace and the construction of the corresponding Wannier functions is a crucial step. Due to the crystal field splitting of the Mn-$3d$ orbitals and their separation from the O-2$p$ bands, SrMnO$_3$ is a material where on first sight a 3-band $d$-only model should be sufficient. However, in the present work we demonstrate that the resulting spectrum is considerably influenced by the number of correlated orbitals and the number of bands included in the Wannier function construction. For example, in a $d$-$dp$ model we observe a splitting of the \tg lower Hubbard band into a more complex spectral structure, not observable in $d$-only models. To illustrate these high-Frequency differences we employ the recently developed Fork Tensor Product State (FTPS) impurity solver, as it provides the necessary spectral resolution on the real-Frequency Axis. We find that the spectral structure of a 5-band $d$-$dp$ model is in good agreement with PES and XAS experiments. Our results demonstrate that the FTPS solver is capable of performing full 5-band DMFT calculations directly on the real-Frequency Axis.
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dynamical mean field theory on the real Frequency Axis p d hybridization and atomic physics in srmno 3
Physical Review B, 2018Co-Authors: D Bauernfeind, Hans Gerd Evertz, Robert Triebl, Manuel Zingl, Markus AichhornAbstract:We investigate the electronic structure of ${\mathrm{SrMnO}}_{3}$ with density functional theory plus dynamical mean-field theory (DMFT). Within this scheme the selection of the correlated subspace and the construction of the corresponding Wannier functions is a crucial step. Due to the crystal-field splitting of the Mn-$3d$ orbitals and their separation from the $\mathrm{O}\text{\ensuremath{-}}2p$ bands, ${\mathrm{SrMnO}}_{3}$ is a material where on first sight a three-band $d$-only model should be sufficient. However, in the present work we demonstrate that the resulting spectrum is considerably influenced by the number of correlated orbitals and the number of bands included in the Wannier function construction. For example, in a $d\text{\ensuremath{-}}dp$ model we observe a splitting of the ${t}_{2g}$ lower Hubbard band into a more complex spectral structure, not observable in $d$-only models. To illustrate these high-Frequency differences we employ the recently developed fork tensor product state (FTPS) impurity solver, as it provides the necessary spectral resolution on the real-Frequency Axis. We find that the spectral structure of a five-band $d\text{\ensuremath{-}}dp$ model is in good agreement with PES and XAS experiments. Our results demonstrate that the FTPS solver is capable of performing full five-band DMFT calculations directly on the real-Frequency Axis.
Olle Gunnarsson - One of the best experts on this subject based on the ideXlab platform.
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analytical continuation of imaginary Axis data for optical conductivity
Physical Review B, 2010Co-Authors: Olle Gunnarsson, Maurits W. Haverkort, Giorgio SangiovanniAbstract:We compare different methods for performing analytical continuation of spectral data from the imaginary time or Frequency Axis to the real Frequency Axis for the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$. We compare the maximum entropy (MaxEnt), singular value decomposition (SVD), sampling, and Pad\'e methods for analytical continuation. We also study two direct methods for obtaining $\ensuremath{\sigma}(0)$. For the MaxEnt approach we focus on a recent modification. The data are split up in batches, a separate MaxEnt calculation is done for each batch and the results are averaged. For the problems studied here, we find that typically the SVD, sampling, and modified MaxEnt methods give comparable accuracy while the Pad\'e approximation is usually less reliable.
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Analytical continuation of spectral data from imaginary time Axis to real Frequency Axis using statistical sampling
Physical Review B, 2007Co-Authors: K Kiamars Vafayi, Olle GunnarssonAbstract:We present a method for performing analytical continuation of spectral data from imaginary time to real frequencies based on a statistical sampling method. Compared with the maximum entropy method (MEM), an advantage is that no default model needs to be introduced. For the problems studied here, the statistical sampling method gives comparable or slightly better results than MEM using quite accurate default models.
F Marsiglio - One of the best experts on this subject based on the ideXlab platform.
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eliashberg theory in the weak coupling limit results on the real Frequency Axis
Physical Review B, 2020Co-Authors: Sepideh Mirabi, Rufus Boyack, F MarsiglioAbstract:We formulate and solve the Eliashberg equations on the imaginary Frequency Axis at temperatures below ${T}_{c}$ in the weak-coupling limit. We find an excellent scaling at all temperatures, for a fixed coupling strength, and the normalized order parameter exhibits a BCS-like temperature dependence. The hybrid real-imaginary Axis equations are also solved to obtain numerically exact analytic continuations from the imaginary Frequency Axis to the real Frequency Axis. This provides a determination of the gap edge, which, in the weak-coupling limit, is identical to the order parameter from the imaginary Axis. The analytical result for the zero-temperature gap edge deviates from the BCS result by a factor of $1/\sqrt{e}$, which was also obtained for the transition temperature ${T}_{c}$. We show that the normalized gap function on both the real and imaginary Frequency axes, for an electron-phonon Einstein spectrum $(\ensuremath{\delta}$ function) of a fixed strength, is a universal function of Frequency, independent of temperature. The $1/\sqrt{e}$ correction is a result of this nontrivial Frequency dependence in the gap function. This modification, in the gap edge and in ${T}_{c}$, serves to preserve various dimensionless ratios to their BCS values.
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eliashberg theory in the weak coupling limit results on the real Frequency Axis
arXiv: Superconductivity, 2019Co-Authors: Sepideh Mirabi, Rufus Boyack, F MarsiglioAbstract:We formulate and solve the Eliashberg equations on the imaginary Frequency Axis at temperatures below $T_c$ in the weak-coupling limit. We find an excellent scaling at all temperatures, for a given coupling strength, and the normalized order parameter exhibits a BCS-like temperature dependence. The hybrid real-imaginary Axis equations are also solved to obtain numerically exact analytic continuations from the imaginary Frequency Axis to the real Frequency Axis. This provides a determination of the gap edge, which, in the weak-coupling limit, is identical to the order parameter from the imaginary Axis. The analytical result for the zero-temperature gap edge deviates from the BCS result by a factor of $1/\sqrt{e}$, which was also obtained for the transition temperature $T_c$. We show that the normalized gap function on both the real and imaginary Frequency axes, for an electron-phonon Einstein spectrum ($\delta$-function) of a given strength, is a universal function of Frequency, independent of temperature. The $1/\sqrt{e}$ correction is a result of this non-trivial Frequency dependence in the gap function. This modification, in the gap edge and in $T_{c}$, serves to preserve various dimensionless ratios to their BCS values.