[QE-users] cRPA - how to get Hubbard U and Hund's J

Cococcioni Matteo matteo.cococcioni at epfl.ch
Thu Nov 22 12:14:48 CET 2018

Dear Chris,

On Nov 22, 2018, at 8:09 AM, Christoph Wolf <wolf.christoph at qns.science<mailto:wolf.christoph at qns.science>> wrote:

Dear all,

I know how to calculate Hubbard U from the linear response mechanism but I found that this is apparently not feasible for J;

"However, this calculation has not been actually attempted yet and it is impossible to comment on its reliability" (https://www.cond-mat.de/events/correl12/manuscripts/cococcioni.pdf)

I have not found a way to compute J from the same LRT that is used to evaluate U. The straightforward extension of the approach to compute U (through perturbing on-site magnetization) is possible in QE (that’s what Hubbard_beta is for) but I was not able to obtain reliable results. I have not had a chance to work much on this so I cannot tell you more.
Perhaps you could estimate J by computing U for a magnetic ground state and for a non-magnetic one and taking the difference between the two values. However this is not completely right as the two ground states are different and, presumably, screening would be different too.

I was curious if there is any other way to get U and J, I know some codes have implemented schemes in the constrained RPA way but how could one get this from QE?

I’m not aware of any attempt to use QE for cRPA calculations of U and J.

However I would like to mention that we have recently completed an implementation of the LRT approach that, based on DFPT, is more efficient, scalable and more user friendly than the one based on supercells. You can find the details in PRB 98, 085127 (2018).
An initial implementation of this reciprocal-space approach will become available with one of the next releases of QE.



Thanks in advance for your help!


Postdoctoral Researcher
Center for Quantum Nanoscience, Institute for Basic Science
Ewha Womans University, Seoul, South Korea
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Matteo Cococcioni
Theory and Simulation of Materials
École Polytechnique Fédérale de Lausanne

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