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Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories

John Perdew1,2, Adrienn Ruzsinszky1, Jianwei Sun3, Niraj Nepal1, Aaron Kaplan1*

1 Department of Physics, Temple University, Philadelphia, PA 19122

2 Department of Chemistry, Temple University, Philadelphia, PA 19122

3 Department of Physics, Tulane University, New Orleans, LA 70118

* Corresponding authors emails: kaplan@temple.edu
DOI10.24435/materialscloud:vh-wc [version v3]

Publication date: Dec 30, 2020

How to cite this record

John Perdew, Adrienn Ruzsinszky, Jianwei Sun, Niraj Nepal, Aaron Kaplan, Interpretations of ground-state symmetry breaking and strong correlation in wavefunction and density functional theories, Materials Cloud Archive 2020.173 (2020), doi: 10.24435/materialscloud:vh-wc.

Description

Strong correlations within a symmetry-unbroken ground-state wavefunction can show up in approximate density functional theory as symmetry-broken spin-densities or total densities, which are sometimes observable. They can arise from soft modes of fluctuations (sometimes collective excitations) such as spin-density or charge-density waves at non-zero wavevector. In this sense, an approximate density functional for exchange and correlation that breaks symmetry can be more revealing (albeit less accurate) than an exact functional that does not. The examples discussed here include the stretched H2 molecule, antiferromagnetic solids, and the static charge-density wave/Wigner crystal phase of a low-density jellium. Time-dependent density functional theory is used to show quantitatively that the static charge density wave is a soft plasmon. More precisely, the frequency of a related density fluctuation drops to zero, as found from the frequency moments of the spectral function, calculated from a recent constraint-based wavevector- and frequency-dependent jellium exchange-correlation kernel. This record contains all raw data used in this project. The second version contains better-converged data for the frequency moments. The parameters used to generate this data are included in a text file. The third version includes third moment sum rule data that is more stable (a typo in the spline interpolation was rectified, see the Gitlab commit record for more detailed information), as well as expanded correlation energy per electron data. The MCP07 analytic continuation to imaginary frequencies is also more correctly treated in this new data set.

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Files

File name Size Description
4.0_moments.csv
MD5md5:c9185e51a680a36a3e514bfe4c5f8ebc
26.5 KiB Zeroth (spectral function), first, and second frequency moments for a bulk jellium of rs = 4, using the dynamic XC MCP07 kernel
69.0_moments.csv
MD5md5:c3520280f04c46955fefc2bc36d24a23
26.9 KiB Zeroth (spectral function), first, and second frequency moments for a bulk jellium of rs = 69, using the dynamic XC MCP07 kernel.
rs_4.0_third_moment_sum_rule.csv
MD5md5:36b326b5f80708b844ee2ad249764617
19.8 KiB Comparison of the third-frequency moment computed directly and extracted via the known sum rule on the XC spectral function (using PW92 approximation for interacting kinetic energy). Bulk jellium, rs = 4.
rs_69.0_third_moment_sum_rule.csv
MD5md5:ad3ff1ea34c9594c351c896a242b81a6
20.5 KiB Comparison of the third-frequency moment computed directly and extracted via the known sum rule on the XC spectral function (using PW92 approximation for interacting kinetic energy). Bulk jellium, rs = 69.
epsilon_C_MCP07.csv
MD5md5:ac8166225f6b8fd24eeee20a9d990337
4.4 KiB Correlation energy per particle in bulk jellium using the dynamic MCP07 kernel
epsilon_C_MCP07_static.csv
MD5md5:dd78c82251e1494bddfbd4ec1c4ea7e4
4.4 KiB Correlation energy per particle in bulk jellium using the static MCP07 kernel
epsilon_C_ALDA.csv
MD5md5:ad3618e10bdad1302bce161bbd74abe2
1.9 KiB Correlation energy per particle in bulk jellium using the adiabatic local density approximation (ALDA).
epsilon_C_RPA.csv
MD5md5:a27cea9c77fa20e51076599cb93b7fe0
6.5 KiB Correlation energy per particle in bulk jellium using the random phase approximation (RPA)
readme.txt
MD5md5:b16bfde0e91c95b3edd09be70abcb2fd
610 Bytes Description of parameters needed to generate these results. Also reflected in the Gitlab repo settings.py file.

License

Files and data are licensed under the terms of the following license: Creative Commons Attribution 4.0 International.
Metadata, except for email addresses, are licensed under the Creative Commons Attribution Share-Alike 4.0 International license.

Keywords

Density functional theory Time-dependent density functional theory jellium exchange-correlation kernel