add a tutorial for SSH model ground state

example/ssh.py

@@ -0,0 +1,155 @@
+"""
+A Tutorial for the Optical SSH Model Ground State Proper
+"""
+import numpy
+import h5py
+from renormalizer.model.model import Model, construct_j_matrix
+from renormalizer.model.basis import BasisSimpleElectron, BasisSHO
+from renormalizer.model.op import Op
+from renormalizer.utils import Quantity
+from renormalizer.mps import Mps, Mpo
+from renormalizer.mps.gs import optimize_mps
+
+
+class OpticalSSHModelGroundState():
+    r"""
+    Ground state properties for the optical SSH model.
+    Hamiltonian:
+    He = sum_{i} t a^\dagger_i a_{i+1}+a_{i+1}^\dagger a_i
+    Hph = sum_i w_0 b^\dagger_i b_i
+    Heph = sum_{i} g (a^\dagger_i+1 a_i + a^\dagger_i a_{i+1}) (X_{i+1} - X_i)
+    X_i = b^\dagger_i + b_i
+    """
+    def __init__(self, params):
+        # Model parameters
+        self.mol_num = params['nsites']
+        self.g = params['g']
+        self.w0 = params['w0']
+        self.nboson_max = params['nboson_max']
+        self.bond_dim = params['bond_dim']
+        self.nsweeps = params['nsweeps']
+        self.periodic = params['periodic']
+        self.t = params['t']
+
+        # Construct hopping matrix
+        j_matrix = construct_j_matrix(self.mol_num, Quantity(self.t), self.periodic)
+
+        # Initialize model with basis and Hamiltonian
+        self.model = self._construct_model(j_matrix)
+
+    def _construct_model(self, j_matrix):
+        # Construct basis
+        basis = []
+        for imol in range(self.mol_num):
+            basis.append(BasisSimpleElectron(imol))
+            basis.append(BasisSHO((imol, 0), self.w0, self.nboson_max))
+
+        # Construct Hamiltonian terms
+        ham = []
+        # Electronic hopping terms
+        for imol in range(self.mol_num):
+            for jmol in range(self.mol_num):
+                if j_matrix[imol, jmol] != 0:
+                    ham.append(Op(r"a^\dagger a", [imol, jmol], j_matrix[imol, jmol]))
+
+        # Bosonic terms
+        for imol in range(self.mol_num):
+            ham.append(Op("b^\dagger b", (imol, 0), self.w0))
+
+        # Electron-phonon coupling
+        ham.extend(self._construct_eph_terms())
+
+        return Model(basis, ham)
+
+    def _construct_eph_terms(self):
+        eph_terms = []
+        # Bulk terms
+        for imol in range(self.mol_num-1):
+            eph_terms.extend([
+                Op(r"a^\dagger a", [imol, imol+1], self.g) * Op("b^\dagger+b", (imol+1, 0)),
+                Op(r"a^\dagger a", [imol, imol+1], -self.g) * Op("b^\dagger+b", (imol, 0)),
+                Op(r"a^\dagger a", [imol+1, imol], self.g) * Op("b^\dagger+b", (imol+1, 0)),
+                Op(r"a^\dagger a", [imol+1, imol], -self.g) * Op("b^\dagger+b", (imol, 0))
+            ])
+
+        # Boundary terms (if periodic)
+        if self.periodic:
+            eph_terms.extend([
+                Op(r"a^\dagger a", [self.mol_num-1, 0], self.g) * Op("b^\dagger+b", (0, 0)),
+                Op(r"a^\dagger a", [self.mol_num-1, 0], -self.g) * Op("b^\dagger+b", (self.mol_num-1, 0)),
+                Op(r"a^\dagger a", [0, self.mol_num-1], self.g) * Op("b^\dagger+b", (0, 0)),
+                Op(r"a^\dagger a", [0, self.mol_num-1], -self.g) * Op("b^\dagger+b", (self.mol_num-1, 0))
+            ])
+        return eph_terms
+
+    def get_gs_energy(self):
+        # Initialize random MPS and construct MPO
+        mps = Mps.random(self.model, 1, self.bond_dim, percent=1.0)
+        mpo = Mpo(self.model)
+
+        # Setup optimization procedure
+        procedure = [
+            [self.bond_dim//4, 0.4],
+            [self.bond_dim//2, 0.2], 
+            [3*self.bond_dim//4, 0.1]
+        ] + [[self.bond_dim, 0]] * (self.nsweeps - 3)
+        mps.optimize_config.procedure = procedure
+        mps.optimize_config.method = "2site"
+
+        # Optimize ground state
+        energies, mps = optimize_mps(mps.copy(), mpo)
+
+        # Calculate observables
+        results = {
+            'energies': energies,
+            'edof_rdm': mps.calc_edof_rdm(),
+            'phonon_occupations': mps.ph_occupations,
+            'phonon_displacement': self.calc_phonon_displacement(mps),
+            'ni_nj': self.calc_ni_nj(mps)
+        }
+
+        return results
+
+    def calc_ni_nj(self, mps):
+        """Calculate density-density correlation function."""
+        ni_nj = numpy.zeros((self.mol_num, self.mol_num))
+        for imol in range(self.mol_num):
+            for jmol in range(self.mol_num):
+                ni = Mpo(self.model, Op("a^\dagger a", [imol, imol]))
+                nj = Mpo(self.model, Op("a^\dagger a", [jmol, jmol]))
+                mpo = ni @ nj
+                ni_nj[imol, jmol] = mps.expectation(mpo)
+        return ni_nj
+
+    def calc_phonon_displacement(self, mps):
+        """Calculate phonon displacement for each site."""
+        phonon_displacement = numpy.zeros(self.mol_num)
+        for imol in range(self.mol_num):
+            mpo = Mpo(self.model, Op("b^\dagger+b", (imol, 0)))
+            phonon_displacement[imol] = mps.expectation(mpo)
+        return phonon_displacement
+
+
+if __name__ == '__main__':
+    import sys 
+    # Model parameters
+    params = {
+        "nsites": 32,
+        'g': 0.7,
+        'w0': 0.5,
+        't': -1.0,
+        'nboson_max': 40,
+        'bond_dim': 128,
+        'nsweeps': 20,
+        'periodic': True
+    }
+
+    # Ground state calculation
+    job = OpticalSSHModelGroundState(params)
+    results = job.get_gs_energy()
+
+    # Save results
+    with h5py.File('gs.h5', 'w') as f:
+        for key, value in results.items():
+            f.create_dataset(key, data=value)
+        f.create_dataset('gs_energy', data=min(results['energies']))