TBTK
ChebyshevExpander

Hamiltonian

\(H = -\mu\sum_{\mathbf{i}}c_{\mathbf{i}}^{\dagger}c_{\mathbf{i}} + t\sum_{\langle \mathbf{i}\mathbf{j}\rangle}c_{\mathbf{i}}^{\dagger}c_{\mathbf{j}}\)

Code

#include "TBTK/PropertyExtractor/ChebyshevExpander.h"
#include "TBTK/Smooth.h"
#include "TBTK/Solver/ChebyshevExpander.h"
#include "TBTK/TBTK.h"
#include "TBTK/Visualization/MatPlotLib/Plotter.h"
#include <complex>
using namespace std;
using namespace TBTK;
using namespace Visualization::MatPlotLib;
complex<double> i(0, 1);
int main(){
//Initialize TBTK.
//Parameters.
const unsigned int SIZE_X = 40;
const unsigned int SIZE_Y = 40;
const double t = -1;
const double mu = 0;
//Set up the Model.
Model model;
for(unsigned int x = 0; x < SIZE_X; x++){
for(unsigned int y = 0; y < SIZE_Y; y++){
if(x+1 < SIZE_X){
model << HoppingAmplitude(
t,
{x+1, y},
{x, y}
) + HC;
}
if(y+1 < SIZE_Y){
model << HoppingAmplitude(
t,
{x, y+1},
{x, y}
) + HC;
}
}
}
model.construct();
//Set up the Solver.
const double SCALE_FACTOR = 5;
const unsigned int NUM_COEFFICIENTS = 500;
solver.setModel(model);
solver.setScaleFactor(SCALE_FACTOR);
solver.setNumCoefficients(NUM_COEFFICIENTS);
solver.setUseLookupTable(true);
//Set up the PropertyExtractor.
const unsigned int ENERGY_RESOLUTION = 1000;
PropertyExtractor::ChebyshevExpander propertyExtractor(solver);
propertyExtractor.setEnergyWindow(
-SCALE_FACTOR,
SCALE_FACTOR,
ENERGY_RESOLUTION
);
//Calculate the local density of states(LDOS).
Property::LDOS ldos = propertyExtractor.calculateLDOS({{_a_, _a_}});
//Plot the LDOS.
Plotter plotter;
plotter.plot({_a_, SIZE_Y/2}, ldos);
plotter.save("figures/LDOS.png");
}

Output

ExamplesChebyshevExpanderLDOS.png