From 0db7facf4bf176756d0fabb7263c3ce578ba9828 Mon Sep 17 00:00:00 2001 From: Antonio Manesco <am@antoniomanesco.org> Date: Sun, 11 Feb 2024 02:54:31 +0100 Subject: [PATCH] add constant term --- codes/hf.py | 9 +++++- examples/tEnergyTest.ipynb | 57 ++++++++++++++++++++++++++++---------- 2 files changed, 51 insertions(+), 15 deletions(-) diff --git a/codes/hf.py b/codes/hf.py index 4ea39fa..860fd87 100644 --- a/codes/hf.py +++ b/codes/hf.py @@ -101,14 +101,21 @@ def compute_mf(rho, H_int): if dim > 0: H0_int = H_int[*([0]*dim)] + rho0 = rho[*([0]*dim)] local_density = np.diag(np.average(rho, axis=tuple([i for i in range(dim)]))) exchange_mf = convolution(rho, H_int) * nk ** (-dim) direct_mf = np.diag(np.einsum("i,ij->j", local_density, H0_int)) + dc_energy_direct = np.einsum("i, j, ij->", local_density, local_density, H0_int) + dc_energy_cross = np.einsum("ij, ji, ij->", H0_int, rho0, rho0) + dc_energy = 2 * dc_energy_direct - dc_energy_cross else: local_density = np.diag(rho) exchange_mf = rho * H_int direct_mf = np.diag(np.einsum("i,ij->j", local_density, H_int)) - return direct_mf - exchange_mf + dc_energy_direct = np.diag(np.einsum("ij, i, j->", H_int, local_density, local_density)) + dc_energy_cross = np.diag(np.einsum("ij, ij, ji->", H_int, rho, rho)) + dc_energy = 2 * dc_energy_direct - dc_energy_cross + return direct_mf - exchange_mf - dc_energy def total_energy(h, rho): """ diff --git a/examples/tEnergyTest.ipynb b/examples/tEnergyTest.ipynb index a0baa48..4ae0164 100644 --- a/examples/tEnergyTest.ipynb +++ b/examples/tEnergyTest.ipynb @@ -18,7 +18,7 @@ "outputs": [], "source": [ "U0 = 1\n", - "nk = 100\n", + "nk = 300\n", "filling = 2\n", "\n", "hopp = np.kron(np.array([[0, 1], [0, 0]]), np.eye(2))\n", @@ -40,7 +40,7 @@ }, { "cell_type": "code", - "execution_count": 5, + "execution_count": 3, "metadata": {}, "outputs": [], "source": [ @@ -64,6 +64,7 @@ "\n", " return tb_mf_k - EF * np.eye(hamiltonians_0.shape[-1]), densityMatrix\n", "\n", + "\n", "tb_mf0, densityMatrix0 = groundstate(U0)\n", "mf0 = tb_mf0 - hamiltonians_0\n", "\n", @@ -74,27 +75,47 @@ " vals, vecs = np.linalg.eigh(hamiltonian)\n", " EF = utils.get_fermi_energy(vals, filling)\n", " densityMatrix = hf.density_matrix(vals, vecs, EF)\n", - " return hf.total_energy(tb_mf0, densityMatrix)" + " return hf.total_energy(\n", + " hamiltonians_0 + mf0 * np.sign(alpha), densityMatrix\n", + " )" ] }, { "cell_type": "code", - "execution_count": 8, + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { + "image/png": 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", "text/plain": [ - "<matplotlib.legend.Legend at 0x123524050>" + "<Figure size 640x480 with 1 Axes>" ] }, - "execution_count": 8, "metadata": {}, - "output_type": "execute_result" - }, + "output_type": "display_data" + } + ], + "source": [ + "alphas = np.linspace(-3, 3, 401)\n", + "plt.plot(alphas, mfRescaled(alphas))\n", + "plt.plot(-alphas, mfRescaled(alphas))\n", + "plt.axvline(x=1, c=\"k\", ls=\"--\")\n", + "plt.axvline(x=-1, c=\"k\", ls=\"--\")\n", + "plt.ylabel(\"Total Energy\")\n", + "plt.xlabel(r\"$\\alpha$\")\n", + "plt.ylim(-4.6, -4.5)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ { "data": { - "image/png": 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", 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] @@ -104,14 +125,22 @@ } ], "source": [ - "alphas = np.linspace(0.5, 1.5, 21)\n", - "plt.plot(alphas, mfRescaled(alphas))\n", + "plt.plot(alphas[:-1], np.diff(mfRescaled(alphas)))\n", + "plt.plot(-alphas[:-1], -np.diff(mfRescaled(alphas)))\n", + "plt.axhline(0, ls='--', c='k')\n", "plt.axvline(x=1, c=\"k\", ls=\"--\")\n", - "plt.ylabel(\"Total Energy\")\n", - "plt.xlabel(r\"$\\alpha$\")\n", - "plt.legend()" + "plt.axvline(x=-1, c=\"k\", ls=\"--\")\n", + "plt.ylim(-1e-3, 1e-3)\n", + "plt.show()" ] }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, { "cell_type": "code", "execution_count": null, -- GitLab