TBTK
BlockDiagonalizer

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/Model.h"
#include "TBTK/PropertyExtractor/BlockDiagonalizer.h"
#include "TBTK/Range.h"
#include "TBTK/Smooth.h"
#include "TBTK/Solver/BlockDiagonalizer.h"
#include "TBTK/Streams.h"
#include "TBTK/TBTK.h"
#include "TBTK/Visualization/MatPlotLib/Plotter.h"
#include <complex>
#include <cmath>
using namespace std;
using namespace TBTK;
using namespace Visualization::MatPlotLib;
int main(){
//Initialize TBTK.
//Parameters.
const int NUM_K_POINTS = 10000;
double a = 1;
//Set up the Model.
Model model;
Range K(0, 2*M_PI, NUM_K_POINTS);
for(int k = 0; k < NUM_K_POINTS; k++)
model << HoppingAmplitude(cos(K[k]*a), {k, 0}, {k, 1}) + HC;
model.setChemicalPotential(-0.5);
model.setTemperature(300);
model.construct();
//Set up the Solver.
solver.setModel(model);
solver.run();
//Set up the PropertyExtractor.
const double LOWER_BOUND = -2;
const double UPPER_BOUND = 2;
const int RESOLUTION = 200;
PropertyExtractor::BlockDiagonalizer propertyExtractor(solver);
propertyExtractor.setEnergyWindow(
LOWER_BOUND,
UPPER_BOUND,
RESOLUTION
);
//Calculate the density of states (DOS).
Property::DOS dos = propertyExtractor.calculateDOS();
//Smooth the DOS
const double SMOOTHING_SIGMA = 0.01;
const unsigned int SMOOTHING_WINDOW = 51;
dos = Smooth::gaussian(dos, SMOOTHING_SIGMA, SMOOTHING_WINDOW);
//Plot the DOS.
Plotter plotter;
plotter.plot(dos);
plotter.save("figures/DOS.png");
//Caluclate the density (momentum space density).
Property::Density density = propertyExtractor.calculateDensity({
//All k-points, summing over the second subindex.
{_a_, IDX_SUM_ALL}
});
//Plot the Density.
plotter.clear();
plotter.setAxes({{0, {0, 2*M_PI}}});
plotter.plot({_a_, IDX_SUM_ALL}, density);
plotter.setLabelX("k");
plotter.save("figures/Density.png");
}

Output

ExamplesBlockDiagonalizerDOS.png
ExamplesBlockDiagonalizerDensity.png