diff --git a/examples/tEnergyTest.ipynb b/examples/tEnergyTest.ipynb index dad50e2dd6bf3f4baffb49287020ce09c5bdd266..952efb5171be61c433c6004589334d65b4f5843c 100644 --- a/examples/tEnergyTest.ipynb +++ b/examples/tEnergyTest.ipynb @@ -17,44 +17,41 @@ "metadata": {}, "outputs": [], "source": [ + "U0 = 1\n", + "nk = 100\n", + "filling = 2\n", + "\n", "hopp = np.kron(np.array([[0, 1], [0, 0]]), np.eye(2))\n", "tb_model = {(0,): hopp + hopp.T.conj(), (1,): hopp, (-1,): hopp.T.conj()}\n", "\n", "\n", - "# define interaction\n", - "def intModel(U):\n", - " model = {\n", + "def model_U(U):\n", + " int_model = {\n", " (0,): U * np.kron(np.ones((2, 2)), np.eye(2)),\n", " }\n", - " return model" + " return model.Model(tb_model=tb_model, int_model=int_model)\n", + "\n", + "\n", + "model0 = model_U(U0)\n", + "model0.vectors = [*model0.int_model.keys()]\n", + "model0.random_guess(model0.vectors)\n", + "model0.kgrid_evaluation(nk=100)" ] }, { "cell_type": "code", - "execution_count": 6, + "execution_count": 5, "metadata": {}, - "outputs": [ - { - "name": "stdout", - "output_type": "stream", - "text": [ - "-2.2252238082028337\n" - ] - } - ], + "outputs": [], "source": [ - "U0 = 1\n", - "nk = 100\n", - "filling = 2\n", - "\n", "hamiltonians_0 = utils.kgrid_hamiltonian(\n", " nk=nk, hk=utils.model2hk(tb_model=tb_model), dim=1\n", ")\n", "\n", + "\n", "def groundstate(U):\n", - " tb_mf = model.Model(tb_model=tb_model, int_model=intModel(U))\n", " tb_mf_k = interface.find_groundstate_ham(\n", - " tb_mf,\n", + " model_U(U),\n", " filling=filling,\n", " nk=nk,\n", " solver=solvers.rspace_solver,\n", @@ -65,46 +62,39 @@ " EF = utils.get_fermi_energy(vals, filling)\n", " densityMatrix = hf.density_matrix(vals, vecs, EF)\n", "\n", - " return tb_mf_k, densityMatrix\n", - "\n", - "@np.vectorize\n", - "def groundstateEnergy(U):\n", - " _, densityMatrix = groundstate(U)\n", - " Vk = utils.model2hk(tb_model=intModel(U))\n", - " H_int = utils.kgrid_hamiltonian(nk=nk, hk=Vk, dim=1)\n", - " mf = hf.compute_mf(densityMatrix, H_int)\n", - " return hf.total_energy(mf + hamiltonians_0, densityMatrix)\n", + " return tb_mf_k - EF * np.eye(hamiltonians_0.shape[-1]), densityMatrix\n", "\n", "tb_mf0, densityMatrix0 = groundstate(U0)\n", - "print(groundstateEnergy(U0))\n", + "mf0 = tb_mf0 - hamiltonians_0\n", + "\n", "\n", "@np.vectorize\n", - "def otherEnergy(U):\n", - " # Total Energy with density matrix from the groundstate at U0\n", - " Vk = utils.model2hk(tb_model=intModel(U))\n", - " H_int = utils.kgrid_hamiltonian(nk=nk, hk=Vk, dim=1)\n", - " mf = hf.compute_mf(densityMatrix0, H_int)\n", - " return hf.total_energy(mf + hamiltonians_0, densityMatrix0)" + "def mfRescaled(alpha, mf0=mf0):\n", + " hamiltonian = hamiltonians_0 + mf0 * alpha\n", + " 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)" ] }, { "cell_type": "code", - "execution_count": 9, + "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ - "<matplotlib.legend.Legend at 0x7ff797ad0450>" + "<matplotlib.legend.Legend at 0x111a85f10>" ] }, - "execution_count": 9, + "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { - "image/png": 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", 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", "text/plain": [ "<Figure size 640x480 with 1 Axes>" ] @@ -114,21 +104,13 @@ } ], "source": [ - "U_list = np.linspace(U0 - 0.2, U0 + 0.2, 10)\n", - "plt.plot(U_list, otherEnergy(U_list), label='MF groundstate from U=1')\n", - "plt.plot(U_list, groundstateEnergy(U_list), label='MF groundstate')\n", - "plt.axvline(x=1, c='k', ls='--')\n", - "plt.ylabel('Total Energy')\n", - "plt.xlabel('U')\n", + "alphas = np.linspace(0.5, 1.5, 21)\n", + "plt.plot(alphas, mfRescaled(alphas), label=\"MF groundstate from U=1\")\n", + "plt.axvline(x=1, c=\"k\", ls=\"--\")\n", + "plt.ylabel(\"Total Energy\")\n", + "plt.xlabel(\"U\")\n", "plt.legend()" ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] } ], "metadata": { @@ -147,7 +129,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.11.7" + "version": "3.11.6" } }, "nbformat": 4,