Sparse sampling approach to efficient 
<i>ab initio</i>
 calculations at finite temperature

Li, Jia; Wallerberger, Markus; Chikano, Naoya; Yeh, Chia-Nan; Gull, Emanuel; Shinaoka, Hiroshi

doi:10.1103/physrevb.101.035144

Cited by 94 publications

(107 citation statements)

References 67 publications

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“…were developed to further improve numerical efficiency. [162][163][164] The method provides momentum-and frequency-dependent self-energies in the regime of weak to intermediate coupling strength and was successfully applied to multi-band high-Tc superconductors. [104,153,154] As for future work it might be interesting to extend multiorbital TPSC to study further neighbor interactions as was already done for the single-orbital TPSC [146][147][148] or superconductivity as was already started in ref.…”

Section: Discussionmentioning

confidence: 99%

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Two‐Particle Self‐Consistent Method for the Multi‐Orbital Hubbard Model

2021

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One of the most challenging problems in solid state systems is the microscopic analysis of electronic correlations. A paramount minimal model that encodes correlation effects is the Hubbard Hamiltonian, which—regardless of its simplicity—is exactly solvable only in a few limiting cases and approximate many‐body methods are required for its solution. In this review, an overview on the non‐perturbative two‐particle self‐consistent method (TPSC), which was originally introduced to describe the electronic properties of the single‐band Hubbard model, is presented. A detailed derivation of the multi‐orbital generalization of TPSC is introduced here and particular features of the method on exemplary interacting models in comparison to dynamical mean‐field theory results are discussed.

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Section: Discussionmentioning

confidence: 99%

“…In addition, new numerical techniques were developed to further improve numerical efficiency. [ 162–164 ] The method provides momentum‐ and frequency‐dependent self‐energies in the regime of weak to intermediate coupling strength and was successfully applied to multi‐band high‐Tc superconductors. [ 104,153,154 ]…”

Section: Discussionmentioning

confidence: 99%

Two‐Particle Self‐Consistent Method for the Multi‐Orbital Hubbard Model

2021

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“…While these do not by themselves change the computational and memory complexity of the solver, they yield a significant reduction in the constant associated with the scaling, and should be used in implementations. Also, in the equilibrium case, spectral methods and specialized basis representations have been used to represent Green's functions with excellent efficiency, and their applicability in the nonequilibrium case has not yet been explored [61,[99][100][101][102].…”

Section: Discussionmentioning

confidence: 99%

Low rank compression in the numerical solution of the nonequilibrium Dyson equation

Kaye

Golež

2021

SciPost Phys.

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We propose a method to improve the computational and memory efficiency of numerical solvers for the nonequilibrium Dyson equation in the Keldysh formalism. It is based on the empirical observation that the nonequilibrium Green's functions and self energies arising in many problems of physical interest, discretized as matrices, have low rank off-diagonal blocks, and can therefore be compressed using a hierarchical low rank data structure. We describe an efficient algorithm to build this compressed representation on the fly during the course of time stepping, and use the representation to reduce the cost of computing history integrals, which is the main computational bottleneck. For systems with the hierarchical low rank property, our method reduces the computational complexity of solving the nonequilibrium Dyson equation from cubic to near quadratic, and the memory complexity from quadratic to near linear. We demonstrate the full solver for the Falicov-Kimball model exposed to a rapid ramp and Floquet driving of system parameters, and are able to increase feasible propagation times substantially. We present examples with 262 144 time steps, which would require approximately five months of computing time and 2.2 TB of memory using the direct time stepping method, but can be completed in just over a day on a laptop with less than 4 GB of memory using our method. We also confirm the hierarchical low rank property for the driven Hubbard model in the weak coupling regime within the GW approximation, and in the strong coupling regime within dynamical mean-field theory.

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“…We have confirmed that the difference of J i j values at β = 200 and 400 eV −1 is less than 1%. We use the intermediate representation basis for the Matsubara frequency summation [79][80][81] and set the cutoff parameter = 10 5 , which is sufficiently larger than W β, where W is the bandwidth.…”

Section: E Calculation Conditionsmentioning

confidence: 99%

Magnetic exchange coupling in cuprate-analog d9 nickelates

Nomura

Nomoto

Hirayama

et al. 2020

Phys. Rev. Research

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Motivated by the recent discovery of superconductivity in doped NdNiO 2 , we study the magnetic exchange interaction J in layered d 9 nickelates from first principles. The mother compounds of the high-T c cuprates belong to the charge-transfer regime in the Zaanen-Sawatzky-Allen diagram and have J larger than 100 meV. While this feature makes the cuprates very different from other transition metal oxides, it is of great interest whether layered d 9 nickelates can also have such a large J. However, one complexity is that NdNiO 2 is not a Mott insulator due to carrier doping from the block layer. To compare the cuprates and d 9 nickelates on an equal basis, we study RbCa 2 NiO 3 and A 2 NiO 2 Br 2 (A denotes a cation with a valence of 2.5+), which were recently designed theoretically by block-layer engineering. These nickelates are free from the self-doping effect and belong to the Mott-Hubbard regime. We show that these nickelates share a common thread with the high-T c cuprates in that they also have a significant exchange interaction J as large as about 100 meV.

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Sparse sampling approach to efficient ab initio calculations at finite temperature

Cited by 94 publications

References 67 publications

Two‐Particle Self‐Consistent Method for the Multi‐Orbital Hubbard Model

Two‐Particle Self‐Consistent Method for the Multi‐Orbital Hubbard Model

Low rank compression in the numerical solution of the nonequilibrium Dyson equation

Magnetic exchange coupling in cuprate-analog d9 nickelates

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