91 lines
2.2 KiB
Matlab
91 lines
2.2 KiB
Matlab
%% STRIPES
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% 2-D
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% Parameters
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c = 1; % Fourier coeffecient
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k = 2; % wavenumber
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n = 2; % order
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% Range for x and y
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x = linspace(-2, 2, 500);
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y = linspace(-2, 2, 500);
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% Create a meshgrid for 2D
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[~, Y] = meshgrid(x, y);
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% Define the 2D function
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f_xy = (1 + (c * cos(n * k * Y))) / (1 + (0.5 * c^2));
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% Plot the 2D image using imagesc
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figure(1);
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imagesc(x, y, f_xy);
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axis xy; % Make sure the y-axis is oriented correctly
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colorbar;
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xlabel('$x l_o$', 'Interpreter', 'latex', 'FontSize', 14)
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ylabel('$y l_o$', 'Interpreter', 'latex', 'FontSize', 14)
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title('Stripe Lattice ansatz for $|\Psi(x,y)|^2$', 'Interpreter', 'latex', 'FontSize', 16);
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xlabel('x');
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ylabel('y');
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colormap parula;
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%% TRIANGULAR LATTICE
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% 2-D
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% Parameters
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c1 = 0.2;
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c2 = 0.2;
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k = 3;
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n = 1;
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% Range for x and y
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x = linspace(-2, 2, 500);
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y = linspace(-2, 2, 500);
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% Create a meshgrid for 2D
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[X, Y] = meshgrid(x, y);
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% Define the 2D function for a triangular lattice
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f_xy = 1 + (c1 * cos(n * k * (2/sqrt(3)) * Y)) + (2 * c2 * cos(n * k * (1/sqrt(3)) * Y) .* cos(n * k * X));
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% Plot the 2D image using imagesc
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figure(2);
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clf
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imagesc(x, y, f_xy);
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axis xy; % Make sure the y-axis is oriented correctly
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colorbar;
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xlabel('$x l_o$', 'Interpreter', 'latex', 'FontSize', 14)
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ylabel('$y l_o$', 'Interpreter', 'latex', 'FontSize', 14)
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title('Triangular Lattice ansatz for $|\Psi(x,y)|^2$', 'Interpreter', 'latex', 'FontSize', 16);
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xlabel('x');
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ylabel('y');
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colormap parula;
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%% HONEYCOMB LATTICE
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% 2-D
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% Parameters
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c1 = 0.2;
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c2 = 0.2;
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k = 3;
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n = 1;
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% Range for x and y
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x = linspace(-2, 2, 500);
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y = linspace(-2, 2, 500);
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% Create a meshgrid for 2D
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[X, Y] = meshgrid(x, y);
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% Define the 2D function for a honeycomb lattice
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f_xy = 1 - (c1 * cos(n * k * (2/sqrt(3)) * X)) - (2 * c2 * cos(n * k * (1/sqrt(3)) * X) .* cos(n * k * Y));
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% Plot the 2D image using imagesc
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figure(3);
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clf
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imagesc(x, y, f_xy);
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axis xy; % Make sure the y-axis is oriented correctly
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colorbar;
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xlabel('$x l_o$', 'Interpreter', 'latex', 'FontSize', 14)
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ylabel('$y l_o$', 'Interpreter', 'latex', 'FontSize', 14)
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title('Honeycomb Lattice ansatz for $|\Psi(x,y)|^2$', 'Interpreter', 'latex', 'FontSize', 16);
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xlabel('x');
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ylabel('y');
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colormap parula;
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