Wolfram Language Paclet Repository
Community-contributed installable additions to the Wolfram Language
QuantumMob`Q3mini`
WickMonitor  |  |
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Details and Options
Examples
(10)
Basic Examples
(2)
Consider some fermion modes.
In[1]:=
$n=4;
Construct a Hamiltonian.
In[2]:=
SeedRandom[370];
In[3]:=
ham=RandomWickHermitian[$n]ham//ArrayShort
Out[3]=
WickHermitian
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Out[3]//MatrixForm=
0 | -0.607449 | 0.179529 | -0.400114 | … |
0.607449 | 0 | -0.3022 | -0.990884 | … |
-0.179529 | 0.3022 | 0 | -0.208244 | … |
0.400114 | 0.990884 | 0.208244 | 0 | … |
… | … | … | … | … |
Set an initial state.
In[4]:=
in=WickState[{1,0},$n];
Do the Monte Carlo simulation.
In[5]:=
SeedRandom[378];
In[6]:=
EchoTiming[data=WickMonitor[in,ham,{$T=2,$dt=0.01},"Samples"150]];Dimensions[data]
⌚
0.818982
Out[6]=
{150,201}
Now, Let us examine the entanglement properties of the data.
First, choose the subsystem.
In[1]:=
kk=Range[$n/2]
Out[1]=
{1,2}
In[2]:=
EchoTiming[ee=WickEntanglementEntropy[data,kk]];Dimensions[ee]
⌚
2.10982
Out[2]=
{150,201}
In[3]:=
ListLinePlot[Mean@ee,DataRange{0,$T},PlotMarkersAutomatic,FrameLabel{"γ","〈EE (, /2)〉"}]
t
L
L
Out[3]=
Construct approximate density matrices, and calculate the (LN) between the subsystem and the rest.
In[4]:=
EchoTiming[avg=WickMean[data];neg=WickLogarithmicNegativity[avg,kk]];Dimensions[neg]
⌚
0.427877
Out[4]=
{201}
In[5]:=
ListLinePlot[Re@neg,DataRange{0,$T},PlotMarkersAutomatic,FrameLabel{"γ","〈LN (, /2)〉"}]
t
L
L
Out[5]=
Applications
(8)
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