diff --git a/_images/247063f54f818a0408991ce1633921635047225ad9ce1c0ac55998880b0c09b6.png b/_images/247063f54f818a0408991ce1633921635047225ad9ce1c0ac55998880b0c09b6.png new file mode 100644 index 0000000..209e7bf Binary files /dev/null and b/_images/247063f54f818a0408991ce1633921635047225ad9ce1c0ac55998880b0c09b6.png differ diff --git a/_sources/phase_transition.ipynb b/_sources/phase_transition.ipynb index 2ba1a7b..0c33092 100644 --- a/_sources/phase_transition.ipynb +++ b/_sources/phase_transition.ipynb @@ -15,7 +15,7 @@ "metadata": {}, "outputs": [], "source": [ - "from qiskit.quantum_info import Statevector, SparsePauliOp, Operator, partial_trace, entropy, DensityMatrix\n", + "from qiskit.quantum_info import Statevector, SparsePauliOp, Operator \n", "\n", "import itertools as it\n", "import scipy.sparse.linalg as ssla\n", @@ -31,6 +31,133 @@ "from spin_ham import *" ] }, + { + "cell_type": "markdown", + "id": "1242a171", + "metadata": {}, + "source": [ + "## Symmetry protected topological (SPT) phase\n", + "\n", + "one-dimensional cluster-Ising model \n", + "$$H = -\\sum_{i=1}^{N-2} Z_i X_{i+1} Z_{i+2} - h_1 \\sum_{i=1}^N X_i - h_2 \\sum_{i=1}^{N-1} X_iX_{i+1} $$\n", + "\n", + "https://arxiv.org/abs/1810.03787" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "id": "41e3b405", + "metadata": {}, + "outputs": [], + "source": [ + "class Cluster_Ising:\n", + " def __init__(self, n: int, h1, h2, verbose):\n", + " self.n = n\n", + " self.h1 = h1\n", + " self.h2 = h2\n", + " self.verbose = verbose\n", + "\n", + " self.H = SparsePauliOp.from_list([['I'*n, 0]])\n", + "\n", + " for i in range(n-2):\n", + " self.H += SparsePauliOp.from_list([['I'*i + 'ZXZ' + 'I'*(n-i-3), -1]])\n", + " self.H += SparsePauliOp.from_list([['I'*i + 'X' + 'I'*(n-i-1), -h1]])\n", + " self.H += SparsePauliOp.from_list([['I'*i + 'XX' + 'I'*(n-i-2), -h2]])\n", + "\n", + " self.H += SparsePauliOp.from_list([['I'*(n-2)+'XI', -h1], ['I'*(n-1)+'X', -h1]])\n", + " self.H += SparsePauliOp.from_list([['I'*(n-2)+'XX', -h2]])\n", + "\n", + " self.H.simplify()\n", + " order_string = ''\n", + " for i in range(1, n+1):\n", + " if i == 1:\n", + " order_string += 'Z'\n", + " elif i % 2 == 0:\n", + " order_string += 'X'\n", + " elif i == n:\n", + " order_string += 'Z'\n", + " else:\n", + " order_string += 'I'\n", + " if verbose: print('order string: ', order_string)\n", + " self.string_order = SparsePauliOp.from_list([[order_string, 1]])\n" + ] + }, + { + "cell_type": "code", + "execution_count": 87, + "id": "071c0fb0", + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.colors as colors\n", + "\n", + "h1_list = np.linspace(0, 2, 50)\n", + "h2_list = np.linspace(-2, 2, 50)\n", + "h1_mesh , h2_mesh = np.meshgrid(h1_list, h2_list)\n", + "exp_vals = np.zeros((len(h1_list), len(h2_list)), dtype=np.complex128)\n", + "\n", + "for i1, h1 in enumerate(h1_list):\n", + " for i2, h2 in enumerate(h2_list):\n", + " n = 5 # number of spins (should be at least odd number)\n", + " ci = Cluster_Ising(n, h1=h1, h2=h2, verbose=False) # create a cluster Ising model with n spins, h1=1, h2=2\n", + "\n", + " # print(ci.H) # print the Hamiltonian\n", + " # print(ci.string_order) # print the string order operator\n", + "\n", + " # ground state of the Hamiltonian\n", + " gnd_st = np.linalg.eigh(ci.H.to_matrix())[1][:,0]\n", + " ob = ci.string_order.to_matrix()\n", + " exp_val = np.dot(np.conj(gnd_st), np.dot(ob, gnd_st))\n", + " exp_vals[i2, i1] = exp_val\n", + "\n", + "# print(exp_vals)" + ] + }, + { + "cell_type": "code", + "execution_count": 88, + "id": "69dfa1b2", + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0.2, 0.4, 'SPT')" + ] + }, + "execution_count": 88, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "image/png": { + "height": 459, + "width": 584 + } + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots()\n", + "z = np.real(exp_vals)\n", + "c = ax.pcolormesh(h1_mesh, h2_mesh, z, norm=colors.LogNorm(vmin=z.min(), vmax=z.max())) \n", + "fig.colorbar(c, ax=ax) # , extend='max'\n", + "ax.set_xlabel(r'$h_1$')\n", + "ax.set_ylabel(r'$h_2$')\n", + "ax.annotate(r'Paramagnetic', xy=(0.5, 0.8), xycoords='axes fraction', ha='center', fontsize=18, color='white')\n", + "ax.annotate(r'Antiferromagnetic', xy=(0.5, 0.1), xycoords='axes fraction', ha='center', fontsize=18, color='white')\n", + "ax.annotate(r'SPT', xy=(0.2, 0.4), xycoords='axes fraction', ha='center', fontsize=18, color='k')" + ] + }, { "cell_type": "markdown", "id": "25d58748", @@ -130,7 +257,7 @@ ], "metadata": { "kernelspec": { - "display_name": "Python 3.8.8 ('base')", + "display_name": "base", "language": "python", "name": "python3" }, @@ -145,11 +272,6 @@ "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.10.14" - }, - "vscode": { - "interpreter": { - "hash": "4e8ef2f9fcac0817bca9a7ca376f64f20b4df5ea3bf7af756a50bda7d3557ea6" - } } }, "nbformat": 4, diff --git a/phase_transition.html b/phase_transition.html index 1b82e7b..49e0d8d 100644 --- a/phase_transition.html +++ b/phase_transition.html @@ -61,6 +61,8 @@ + + @@ -397,6 +399,7 @@

Contents