TBTK
1D chain

Hamiltonian

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

Code

#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.
//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();
//Set up the 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.
= 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

ExamplesChain1DDOS.png
ExamplesChain1DWaveFunctions.png