A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of...
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A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of Cambridge
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Transcript of A QMC Study of the Homogeneous Electron Gas Graham Spink and Richard Needs, TCM, University of...
A QMC Study of the Homogeneous Electron Gas
Graham Spink and Richard Needs, TCM, University of Cambridge
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 ))(()(][
Pair Correlation Function
RR
RrrR
d
dr
Nrrg 2
21
2
2)(
)()(1
4)(
1
21
21
Momentum Density
R
xRrrrrxrr
k
xk
d
dde
rn
N
i Ni
Nii
s 21 1
12
),,,,(),,,,(
),(
Gori-Giorgi and Ziesche, PRB 66, 235116
“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.,
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
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
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
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
Pair Correlation Function
RR
RrrR
d
dr
Nrrg 2
21
2
2)(
)()(1
4)(
1
21
21
On top pair density
DFT Finite Size Corrections
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
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
