From 78f435df893f37df95ddc3a50c2e492a3064aae6 Mon Sep 17 00:00:00 2001
From: Karthik Chandrashekara <karthik@physi.uni-heidelberg.de>
Date: Fri, 9 May 2025 00:33:03 +0200
Subject: [PATCH] New ansatzes

---
 Estimations/VisualizeCosineModulatedAnsatz.m | 95 ++++++++++++++++++++
 1 file changed, 95 insertions(+)

diff --git a/Estimations/VisualizeCosineModulatedAnsatz.m b/Estimations/VisualizeCosineModulatedAnsatz.m
index f58badb..918591d 100644
--- a/Estimations/VisualizeCosineModulatedAnsatz.m
+++ b/Estimations/VisualizeCosineModulatedAnsatz.m
@@ -195,5 +195,100 @@ colorbar;
 title('Gaussian + Honeycomb lattice');
 xlabel('x'); ylabel('y');
 
+%%
+% Parameters
+A = 1;                  % Modulation amplitude
+p = 2 * pi / 10;        % Magnitude of p_j (adjust wavelength)
+L = 50;                 % Spatial extent
+N = 500;                % Grid resolution
+
+% Coordinate grid
+x = linspace(-L, L, N);
+y = linspace(-L, L, N);
+[X, Y] = meshgrid(x, y);
+
+% Define p_j vectors at 0°, 120°, and 240°
+angles = [0, 2*pi/3, 4*pi/3];
+P = zeros(size(X));
+
+for j = 1:3
+    pj = p * [cos(angles(j)); sin(angles(j))];  % 2D vector
+    dotprod = pj(1) * X + pj(2) * Y;
+    P = P + cos(dotprod);
+end
+
+P = A * P;  % Apply modulation amplitude
+
+% Plot
+figure(20);
+imagesc(x, y, P);
+axis equal tight;
+colormap turbo; colorbar;
+xlabel('$x$', 'Interpreter', 'latex', 'FontSize', 14);
+ylabel('$y$', 'Interpreter', 'latex', 'FontSize', 14);
+title('Triangle Phase: $P(\mathbf{r}_\perp) = A \sum_{j=1}^3 \cos(\mathbf{p}_j \cdot \mathbf{r}_\perp)$', ...
+      'Interpreter', 'latex', 'FontSize', 16);
+
+% Parameters
+A = -1;                  % Modulation amplitude
+p = 2 * pi / 10;        % Magnitude of p_j (adjust wavelength)
+L = 50;                 % Spatial extent
+N = 500;                % Grid resolution
+
+% Coordinate grid
+x = linspace(-L, L, N);
+y = linspace(-L, L, N);
+[X, Y] = meshgrid(x, y);
+r = cat(3, X, Y);
+
+% Define p_j vectors at 0°, 120°, and 240°
+angles = [0, 2*pi/3, 4*pi/3];
+P = zeros(size(X));
+
+for j = 1:3
+    pj = p * [cos(angles(j)); sin(angles(j))];  % 2D vector
+    dotprod = pj(1) * X + pj(2) * Y;
+    P = P + cos(dotprod);
+end
+
+P = A * P;  % Apply modulation amplitude
+
+% Plot
+figure(21);
+imagesc(x, y, P);
+axis equal tight;
+colormap turbo; colorbar;
+xlabel('$x$', 'Interpreter', 'latex', 'FontSize', 14);
+ylabel('$y$', 'Interpreter', 'latex', 'FontSize', 14);
+title('Honeycomb Phase: $P(\mathbf{r}_\perp) = A \sum_{j=1}^3 \cos(\mathbf{p}_j \cdot \mathbf{r}_\perp)$', ...
+      'Interpreter', 'latex', 'FontSize', 16);
+
+% Parameters
+A = 1;                  
+p = 2 * pi / 10;        % Wavevector magnitude
+theta = pi/2;           % Angle of the wavevector (45° for diagonals)
+L = 50;
+N = 500;
+
+% Grid
+x = linspace(-L, L, N);
+y = linspace(-L, L, N);
+[X, Y] = meshgrid(x, y);
+
+% Define wavevector p
+p_vec = p * [cos(theta); sin(theta)];
+
+% Compute density
+P = A * cos(p_vec(1) * X + p_vec(2) * Y);
+
+% Plot
+figure(22);
+imagesc(x, y, P);
+axis equal tight;
+colormap turbo; colorbar;
+xlabel('$x$', 'Interpreter', 'latex', 'FontSize', 14);
+ylabel('$y$', 'Interpreter', 'latex', 'FontSize', 14);
+title('Stripe Phase: $P(\mathbf{r}_\perp) = A \cos(\mathbf{p} \cdot \mathbf{r}_\perp)$', ...
+      'Interpreter', 'latex', 'FontSize', 16);