[tetku.py] Add Gibbs Rydberg model.

Author: hzhangxyz

tetraku/tetraku/models/gibbs_rydberg/__init__.py

@@ -0,0 +1,89 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+# Copyright (C) 2021-2024 Hao Zhang<zh970205@mail.ustc.edu.cn>
+#
+# This program is free software: you can redistribute it and/or modify
+# it under the terms of the GNU General Public License as published by
+# the Free Software Foundation, either version 3 of the License, or
+# any later version.
+#
+# This program is distributed in the hope that it will be useful,
+# but WITHOUT ANY WARRANTY; without even the implied warranty of
+# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+# GNU General Public License for more details.
+#
+# You should have received a copy of the GNU General Public License
+# along with this program.  If not, see <https://www.gnu.org/licenses/>.
+#
+
+import TAT
+import tetragono as tet
+from tetragono.common_tensor.tensor_toolkit import kronecker_product, rename_io
+
+
+def abstract_state(L1, L2, delta, omega, radius, side=1):
+    """
+    Create density matrix of square Rydberg state.
+    see https://arxiv.org/pdf/2112.10790.pdf
+
+    Parameters
+    ----------
+    L1, L2 : int
+        The lattice size.
+    delta, omega, radius : float
+        Rydberg atom parameters.
+    side : 1 | 2, default=1
+        The Hamiltonian should apply to single side or both side of density matrix.
+    """
+    if side not in [1, 2]:
+        raise RuntimeError("side should be either 1 or 2")
+    state = tet.AbstractState(TAT.No.D.Tensor, L1, L2)
+    for layer in (0, 1):
+        for [l1, l2] in state.sites():
+            state.physics_edges[(l1, l2, layer)] = 2
+
+    # hamiltonian
+    sigma = tet.common_tensor.No.pauli_x.to(float)
+    n = (tet.common_tensor.No.identity.to(float) - tet.common_tensor.No.pauli_z.to(float)) / 2
+    single_body_hamiltonian = omega * sigma / 2 - delta * n
+    nn = kronecker_product(rename_io(n, [0]), rename_io(n, [1]))
+    for layer in range(side):
+        # Hamiltonian for the second layer should be transposed
+        # (transpose but not conjugate, or conjugate but not transpose),
+        # But the hamiltonian is real, so nothing to do here
+        for [l1, l2] in state.sites():
+            state.hamiltonians[
+                (l1, l2, layer),
+            ] = single_body_hamiltonian
+        for [al1, al2] in state.sites():
+            for [bl1, bl2] in state.sites():
+                if (al1, al2) >= (bl1, bl2):
+                    continue
+                dl1 = abs(al1 - bl1)
+                dl2 = abs(al2 - bl2)
+                distance = (dl1**2 + dl2**2)**0.5
+                param = (radius / distance)**6
+                state.hamiltonians[(al1, al2, layer), (bl1, bl2, layer)] = omega * param * nn
+    return state
+
+
+def abstract_lattice(L1, L2, D, delta, omega, radius, side=1):
+    """
+    Create density matrix of square Rydberg lattice.
+    see https://arxiv.org/pdf/2112.10790.pdf
+
+    Parameters
+    ----------
+    L1, L2 : int
+        The lattice size.
+    D : int
+        The cut dimension.
+    delta, omega, radius : float
+        Rydberg atom parameters.
+    side : 1 | 2, default=1
+        The Hamiltonian should apply to single side or both side of density matrix.
+    """
+    state = tet.AbstractLattice(abstract_state(L1, L2, delta, omega, radius, side=side))
+    state.virtual_bond["R"] = D
+    state.virtual_bond["D"] = D
+    return state