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.
    Initialize();

    //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::BlockDiagonalizer 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