Electronic Transport as a Driver for Self-Interaction-Corrected Methods

Pertsova, Anna; Canali, Carlo M.; Pederson, Mark R.; Rungger, Ivan; Sanvito, Stefano

doi:10.1016/bs.aamop.2015.06.002

Cited by 8 publications

(8 citation statements)

References 116 publications

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“…Note that in Eqs. ( 9) and (11) we use the fact that the number of electrons of the states in the brackets differs by one. For increasing N imp +N b the total number of excited states M N0±1 becomes exponentially large.…”

Section: A Dynamical Mean Field Theorymentioning

confidence: 99%

“…In our quantum algorithm we determine G α (ω) with calculations on a quantum computer, which means that we evaluate the quantities in Eqs. (8)(9)(10)(11) on a quantum device. The remaining computations of the DMFT calculation are performed on a classical computer (Fig.…”

Section: A Dynamical Mean Field Theorymentioning

confidence: 99%

“…The reason is that DFT treats the quantum mechanical interactions between electrons within an effective mean field approximation, which becomes invalid when the electrons are strongly correlated with each other. A number of corrections have been developed to overcome the limitations of DFT 9 , such as hybrid functionals 10 , self-interaction corrections 11 , or the GW approximation 12 . For solid state systems, where local electron-electron correlations are strong, the dynamical mean field theory (DMFT) is the state-of-the-art correction to DFT [13][14][15] .…”

Section: Introductionmentioning

confidence: 99%

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Dynamical mean field theory algorithm and experiment on quantum computers

Rungger,

Fitzpatrick,

Chen

et al. 2019

Preprint

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The developments of quantum computing algorithms and experiments for atomic scale simulations have largely focused on quantum chemistry for molecules, while their application in condensed matter systems is scarcely explored. Here we present a quantum algorithm to perform dynamical mean field theory (DMFT) calculations for condensed matter systems on currently available quantum computers, and demonstrate it on two quantum hardware platforms. DMFT is required to properly describe the large class of materials with strongly correlated electrons. The computationally challenging part arises from solving the effective problem of an interacting impurity coupled to a bath, which scales exponentially with system size on conventional computers. An exponential speedup is expected on quantum computers, but the algorithms proposed so far are based on real time evolution of the wavefunction, which requires very low noise levels in the quantum hardware. Here we propose an alternative approach, which uses the variational quantum eigensolver (VQE) method for ground and excited states to obtain the needed quantities as part of an exact diagonalization impurity solver. We present the algorithm for a two site DMFT system, which we benchmark using simulations on conventional computers as well as experiments on superconducting and trapped ion qubits, demonstrating that this method is suitable for running DMFT calculations on currently available quantum hardware.

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Section: A Dynamical Mean Field Theorymentioning

confidence: 99%

Section: A Dynamical Mean Field Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamical mean field theory algorithm and experiment on quantum computers

Rungger,

Fitzpatrick,

Chen

et al. 2019

Preprint

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“…DFT methods with a large self-interaction error (local approximations and GGA, for a complete discussion of the influence of this error on tranport calculations see ref. [27]) will result in small energy gaps between empty and occupied orbitals, thus, giving wrong transmission curves and conductance values that are often too large. This can be improved by using more sophisticate functionals that partially remove such error (for instance, hybrid or long-range corrected functionals).…”

Section: Introductionmentioning

confidence: 99%

DFT approaches to transport calculations in magnetic single-molecule devices

2016

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Electron transport properties of single-molecule devices based on the [Fe(tzpy) 2 (NCS) 2 ] complex placed between two gold electrodes have been explored using three different atomistic DFT methods. This kind of single-molecule devices are quite appealing because they can present magnetoresistance effects at room temperature. The three employed computational approaches are:(i) self-consistent non-equilibrium Green functions (NEGF) with periodic models that can be described as the most accurate between the state-of-art methods, and two non self-consistent NEGF approaches using either periodic or non periodic description of the electrodes (ii and iii). The analysis of the transmission spectra obtained with the three methods indicate that they provide similar qualitative results. To obtain a reasonable agreement with the experimental data, it is mandatory to employ density functionals beyond the commonly employed GGA (i.e. hybrid) or to include on-site corrections for the Coulomb repulsion (GGA+U method).

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“…Shortly thereafter, the Wisconsin SIC group [33][34][35] suggested the use of localization-equations as a variational means for addressing the unitary non-invariance that existed in the original formulation. This approach has been the primary means for variational self-interaction corrections as discussed in recent reviews [36][37][38][39][40][41][42][43]. While the original version of SIC [33][34][35] only considered real orbitals, several researchers [40,44,45] have noted that there is no a priori reason to expect that complex orbitals could not lead to lower SIC energies and have derived additional formulae for their minimization.…”

Section: Fermi-löwdin Orbitals For Unitarily Invariant Sicmentioning

confidence: 99%

The Role of Self-Interaction Corrections, Vibrations, and Spin-Orbit in Determining the Ground Spin State in a Simple Heme

et al. 2017

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Without self-interaction corrections or the use of hybrid functionals, approximations to the density-functional theory (DFT) often favor intermediate spin systems over high-spin systems. In this paper, we apply the recently proposed Fermi-Löwdin-orbital self-interaction corrected density functional formalism to a simple tetra-coordinated Fe(II)-porphyrin molecule and show that the energetic orderings of the S = 1 and S = 2 spin states are changed qualitatively relative to the results of Generalized Gradient Approximation (developed by Perdew, Burke, and Ernzerhof, PBE-GGA) and Local Density Approximation (developed by Perdew and Wang, PW92-LDA). Because the energetics, associated with changes in total spin, are small, we have also calculated the second-order spin-orbit energies and the zero-point vibrational energies to determine whether such corrections could be important in metal-substituted porphins. Our results find that the size of the spin-orbit and vibrational corrections to the energy orderings are small compared to the changes due to the self-interaction correction. Spin dependencies in the Infrared (IR)/Raman spectra and the zero-field splittings are provided as a possible means for identifying the spin in porphyrins containing Fe(II).

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Electronic Transport as a Driver for Self-Interaction-Corrected Methods

Cited by 8 publications

References 116 publications

Dynamical mean field theory algorithm and experiment on quantum computers

Dynamical mean field theory algorithm and experiment on quantum computers

DFT approaches to transport calculations in magnetic single-molecule devices

The Role of Self-Interaction Corrections, Vibrations, and Spin-Orbit in Determining the Ground Spin State in a Simple Heme

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