1D chain

Hamiltonian

\(H = -\mu\sum_{x}c_{x}^{\dagger}c_{x} + t\sum_{x}c_{x+1}^{\dagger}c_{x}\)

Code

#include "TBTK/Property/DOS.h"
#include "TBTK/PropertyExtractor/Diagonalizer.h"
#include "TBTK/Smooth.h"
#include "TBTK/Solver/Diagonalizer.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.
    Initialize();
 
    //Parameters.
    const unsigned int SIZE = 500;
    const double t = -1;
    const double mu = -1;
 
    //Set up the Model.
    Model model;
    for(unsigned int x = 0; x < SIZE; x++)
        model << HoppingAmplitude(t, {x+1}, {x}) + HC;
    model.construct();
    model.setChemicalPotential(mu);
 
    //Set up the Solver.
    Solver::Diagonalizer solver;
    solver.setModel(model);
    solver.run();
 
    //Set up the PropertyExtractor.
    const double LOWER_BOUND = -3;
    const double UPPER_BOUND = 3;
    const unsigned int RESOLUTION = 1000;
    PropertyExtractor::Diagonalizer 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 = 0.03;
    const unsigned int SMOOTHING_WINDOW = 101;
    dos = Smooth::gaussian(dos, SMOOTHING_SIGMA, SMOOTHING_WINDOW);
 
    //Plot the DOS.
    Plotter plotter;
    plotter.plot(dos);
    plotter.save("figures/DOS.png");
 
    //Calculate the wave functions.
    Property::WaveFunctions waveFunctions
        = propertyExtractor.calculateWaveFunctions(
            {{_a_}},
            {_a_}
        );
 
    //Plot wave function for state 0, 1, and 2.
    plotter.clear();
    plotter.setTitle("Wave function for state 0, 1, and 2.");
    for(unsigned int state = 0; state < 3; state++)
        plotter.plot({_a_}, state, waveFunctions);
    plotter.save("figures/WaveFunctions.png");
}

Output