a qmc study of the homogeneous electron gas graham spink and richard needs, tcm, university of...
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![Page 1: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/1.jpg)
A QMC Study of the Homogeneous Electron Gas
Graham Spink and Richard Needs, TCM, University of Cambridge
![Page 2: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/2.jpg)
Homogeneous Electron Gas
bbbei ij jii
iHHH
ˆˆ1
2
1
2
1ˆ 2
rr
•Electrons move in uniform, positive background potential:
•Used in Local Density Approximation in DFT:
•Only one independent parameter, rs, the “typical” distance between electrons. ζ is the spin polarization.
rrr dnnnXC
LDA
XCE ))(()(][
![Page 3: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/3.jpg)
Pair Correlation Function
RR
RrrR
d
dr
Nrrg 2
21
2
2)(
)()(1
4)(
1
21
21
![Page 4: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/4.jpg)
Momentum Density
R
xRrrrrxrr
k
xk
d
dde
rn
N
i Ni
Nii
s 21 1
12
),,,,(),,,,(
),(
Gori-Giorgi and Ziesche, PRB 66, 235116
![Page 5: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/5.jpg)
“New” Techniques• More accurate Jastrow factor• Backflow
López Ríos et al., submitted to Phys. Rev. E;
@rs=0.5 increases VMC correlation energy by 5%
• Three-body Jastrow terms Holtzmann et al., Phys. Rev. E 68 046707; @ rs=20, increases VMC correlation energy by over 1%
• Different treatment of finite-size effects Drummond et al.,
![Page 6: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/6.jpg)
PCF Size Convergence
0
0.2
0.4
0.6
0.8
1
1.2
0 0.5 1 1.5 2 2.5 3 3.5
r/rs (a.u.)
Anti-
para
llel s
pin
PCF
rs0.5,118e
rs0.5, 226e
rs20, 118e
rs20, 226e
![Page 7: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/7.jpg)
PCF with Backflow
0
0.2
0.4
0.6
0.8
1
1.2
0 1 2 3 4 5r/rs
anti-
para
llel P
CF
rs0.5;noBF
rs0.5;BFrs20;noBF
rs20;BF
rs3;noBFrs3;BF
![Page 8: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/8.jpg)
Momentum Densityrs=3.0, z=0
-2.00E-01
0.00E+00
2.00E-01
4.00E-01
6.00E-01
8.00E-01
1.00E+00
1.20E+00
0.00E+00 2.00E-01 4.00E-01 6.00E-01 8.00E-01 1.00E+00 1.20E+00 1.40E+00 1.60E+00
q/kF
n(q
)
Ortiz & Ballone
CASINO
![Page 9: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/9.jpg)
PCF at rs=0.5 in VMC and DMC
0.6
0.7
0.8
0.9
1
1.1
0 0.5 1 1.5 2 2.5
r/a.u.
Anti-
para
llel P
CF
DMC
VMC
![Page 10: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/10.jpg)
Pair Correlation Function
RR
RrrR
d
dr
Nrrg 2
21
2
2)(
)()(1
4)(
1
21
21
![Page 11: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/11.jpg)
On top pair density
![Page 12: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/12.jpg)
DFT Finite Size Corrections
![Page 13: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/13.jpg)
Conclusions and Future Work
• New techniques in QMC simulations make significant difference to quantities considered
• With new data we can test recently proposed fitting procedures
• Now continuing the above at intermediate densities and with DMC
![Page 14: A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge](https://reader035.vdocuments.pub/reader035/viewer/2022062516/56649d615503460f94a42493/html5/thumbnails/14.jpg)
Results for PCF
0.000000
0.100000
0.200000
0.300000
0.400000
0.500000
0.600000
0.700000
0.800000
0.900000
1.000000
1.100000
0.000000 1.000000 2.000000 3.000000 4.000000 5.000000 6.000000 7.000000 8.000000
r/a.u.
Without Backflow
With Backflow
PC
F (
anti-
para
llel s
pins
)
VMC, 162 electrons, rs=3.0, ζ=0.0