Merge pull request #131 from BoothGroup/ewdmet_scmf

Implements quasiparticle EWDMET to obtain spectral functions from embedded calculations, making use of the Dyson package for moment based approaches to Green's function calculations.

.gitignore

@@ -145,6 +145,9 @@ pyscf.out
 # Vayesta log files
 vlog.txt
 verr.txt
+f*_pyscf.txt
+f*.out
+*.h5
 
 # HDF5 files
 *.h5

examples/ewdmet/01-sc-qp-ewdmet-hubbard1d-exact-limit.py

@@ -0,0 +1,67 @@
+import numpy as np
+
+import vayesta
+import vayesta.ewf
+from vayesta.lattmod import Hubbard1D, LatticeRHF
+
+from dyson import MBLGF, AuxiliaryShift, FCI, MixedMBLGF, NullLogger, Lehmann
+
+nsite = 10
+nelec = nsite
+u = 6
+nfrag = 2
+
+nmom_max_fci = (4,4)
+nmom_max_bath=1
+
+
+
+
+hubbard = Hubbard1D(nsite=nsite, nelectron=nelec, hubbard_u=u, verbose=0)
+mf = LatticeRHF(hubbard)
+mf.kernel()
+
+# Full system FCI GF
+expr = FCI["1h"](mf)
+th = expr.build_gf_moments(nmom_max_fci[0]) 
+expr = FCI["1p"](mf)
+tp = expr.build_gf_moments(nmom_max_fci[1])
+
+solverh = MBLGF(th, log=NullLogger())
+solverp = MBLGF(tp, log=NullLogger())
+solver = MixedMBLGF(solverh, solverp)
+solver.kernel()
+se = solver.get_self_energy()
+solver = AuxiliaryShift(th[1]+tp[1], se, nelec, log=NullLogger())
+solver.kernel()
+static_potential = se.as_static_potential(mf.mo_energy, eta=1e-2)
+gf = solver.get_greens_function()
+dm = gf.occupied().moment(0) * 2.0
+nelec_gf = np.trace(dm)
+print("Exact GF nelec: %s"%nelec_gf)
+
+sc = mf.get_ovlp() @ mf.mo_coeff
+new_fock = sc @ (th[1] + tp[1] + static_potential) @ sc.T
+e, mo_coeff = np.linalg.eigh(new_fock) 
+chempot = (e[nelec//2-1] + e[nelec//2] ) / 2
+gf_static = Lehmann(e, mo_coeff, chempot=chempot)
+
+gap = lambda gf: gf.physical().virtual().energies[0] - gf.physical().occupied().energies[-1]
+dynamic_gap = gap(gf)
+static_gap = gap(gf_static)
+
+# QP-EwDMET GF
+opts = dict(sc=False, store_hist=True, aux_shift=True, store_scfs=True, diis=True, damping=0, static_potential_conv_tol=1e-6, use_sym=False, eta=1e-2)
+emb = vayesta.ewf.EWF(mf, solver='FCI', bath_options=dict(bathtype='full', dmet_threshold=1e-12), solver_options=dict(conv_tol=1e-15, n_moments=nmom_max_fci))
+emb.qpewdmet_scmf(proj=1, maxiter=10, **opts)
+nimages = [nsite//nfrag, 1, 1]
+emb.symmetry.set_translations(nimages)
+with emb.site_fragmentation() as f:
+    f.add_atomic_fragment(range(nfrag))
+emb.kernel()
+
+emb_dynamic_gap = gap(emb.with_scmf.gf)
+emb_static_gap = gap(emb.with_scmf.gf_qp)
+print("Ran for %s iterations"%emb.with_scmf.iteration)
+print("Dynamic gap, FCI: %s  Emb: %s"%(dynamic_gap, emb_dynamic_gap))
+print("Static  gap, FCI: %s  Emb: %s"%(static_gap, emb_static_gap))

examples/ewdmet/02-sc-qp-ewdmet-hubbard1d-projectors.py

@@ -0,0 +1,65 @@
+import numpy as np
+
+import vayesta
+import vayesta.ewf
+from vayesta.lattmod import Hubbard1D, LatticeRHF
+
+# Plot the spectrum
+from dyson.util import build_spectral_function
+import matplotlib.pyplot as plt
+
+nsite = 12
+nelec = nsite
+nfrag = 2
+u = 3
+
+nmom_max_fci = (4,4)
+nmom_max_bath=1
+
+
+hubbard = Hubbard1D(nsite=nsite, nelectron=nelec, hubbard_u=u, verbose=0)
+mf = LatticeRHF(hubbard)
+mf.kernel()
+
+emb = vayesta.ewf.EWF(mf, solver='FCI', bath_options=dict(bathtype='ewdmet', max_order=1, order=1, dmet_threshold=1e-10), solver_options=dict(conv_tol=1e-12, init_guess='cisd', n_moments=nmom_max_fci))
+nimages = [nsite//nfrag, 1, 1]
+emb.symmetry.set_translations(nimages)
+with emb.site_fragmentation() as f:
+    f.add_atomic_fragment(list(range(nfrag)))
+emb.qpewdmet_scmf(maxiter=100, proj=1)
+emb.kernel()
+gf, gf_qp = emb.with_scmf.get_greens_function()
+
+fig, ax = plt.subplots(2,1, figsize=(16,9))
+
+grid = np.linspace(-5, 11, 1024)
+sf_hf = build_spectral_function(mf.mo_energy, np.eye(mf.mo_occ.size), grid, eta=0.1)
+ax[0].plot(grid, sf_hf, 'r-', label='HF')
+ax[1].plot(grid, sf_hf, 'r-', label='HF')
+
+sf_dynamic = build_spectral_function(gf.energies, gf.couplings, grid, eta=0.1)
+sf_static = build_spectral_function(gf_qp.energies, gf_qp.couplings, grid, eta=0.1)
+ax[0].plot(grid, sf_dynamic, "b-", label="QP-EwDMET (1 Proj, dynamic)")
+ax[1].plot(grid, sf_static, "g-", label="QP-EwDMET (1 Proj, static)")
+
+
+emb = vayesta.ewf.EWF(mf, solver='FCI', bath_options=dict(bathtype='ewdmet', max_order=1, order=1, dmet_threshold=1e-10), solver_options=dict(conv_tol=1e-12, init_guess='cisd', n_moments=nmom_max_fci))
+nimages = [nsite//nfrag, 1, 1]
+emb.symmetry.set_translations(nimages)
+with emb.site_fragmentation() as f:
+    f.add_atomic_fragment(list(range(nfrag)))
+emb.qpewdmet_scmf(maxiter=100, proj=2)
+emb.kernel()
+gf, gf_qp = emb.with_scmf.get_greens_function()
+
+sf_dynamic = build_spectral_function(gf.energies, gf.couplings, grid, eta=0.1)
+sf_static = build_spectral_function(gf_qp.energies, gf_qp.couplings, grid, eta=0.1)
+ax[0].plot(grid, sf_dynamic, "m-", label="QP-EwDMET (2 Proj, dynamic)")
+ax[1].plot(grid, sf_static, "y-", label="QP-EwDMET (2, Proj, static)")
+
+
+ax[0].set_title('U = %d'%u)
+ax[0].legend()
+ax[1].legend()
+
+plt.savefig("hubbard_spectral_function.png")

examples/ewdmet/03-sc-qp-ewdmet-hubbard1d-bethe.py

@@ -0,0 +1,42 @@
+import numpy as np
+import vayesta
+import vayesta.ewf
+from vayesta.lattmod import Hubbard1D, LatticeRHF
+from vayesta.lattmod.bethe import hubbard1d_bethe_gap
+from dyson import Lehmann, FCI, CCSD
+
+u = 3
+nsite = 128
+nelec = nsite
+nfrag = 2
+nmom_max_bath = 1
+nmom_max_fci = (4,4)
+solv = 'FCI'
+EXPR = FCI if solv=='FCI' else CCSD
+hubbard = Hubbard1D(nsite=nsite, nelectron=nelec, hubbard_u=u, verbose=0)
+mf = LatticeRHF(hubbard)
+mf.kernel()
+
+chempot = (mf.mo_energy[nsite//2-1] + mf.mo_energy[nsite//2] ) / 2
+gf_hf = Lehmann(mf.mo_energy, np.eye(mf.mo_coeff.shape[0]), chempot=chempot)
+
+
+emb = vayesta.ewf.EWF(mf, solver=solv, bath_options=dict(bathtype='ewdmet', max_order=nmom_max_bath, order=nmom_max_bath, dmet_threshold=1e-12), solver_options=dict(conv_tol=1e-12, n_moments=nmom_max_fci))
+emb.qpewdmet_scmf(proj=2, maxiter=10)
+nimages = [nsite//nfrag, 1, 1]
+emb.symmetry.set_translations(nimages)
+with emb.site_fragmentation() as f:
+    f.add_atomic_fragment(list(range(nfrag)))
+emb.kernel()
+
+gap = lambda gf: gf.physical().virtual().energies[0] - gf.physical().occupied().energies[-1]
+emb_dynamic_gap = gap(emb.with_scmf.gf)
+emb_static_gap = gap(emb.with_scmf.gf_qp)
+hf_gap = gap(gf_hf)
+bethe_gap = hubbard1d_bethe_gap(1,u, interval=(1,200))
+
+print("Ran for %s iterations"%emb.with_scmf.iteration)
+print("Bethe ansatz gap: %s "%(bethe_gap))
+print("Hartree-Fock gap: %s"%(hf_gap))
+print("Dynamic GF gap:   %s"%(emb_dynamic_gap))
+print("Static GF gap:    %s"%(emb_static_gap))

examples/ewdmet/10-sc-qp-ewdmet-hydrogen-ring-exact-limit.py

@@ -0,0 +1,77 @@
+import numpy as np
+import scipy
+
+import pyscf
+import pyscf.scf
+
+import vayesta
+import vayesta.ewf
+from vayesta.misc.molecules import ring
+from dyson import MBLGF, AuxiliaryShift, FCI, MixedMBLGF, NullLogger, Lehmann
+from dyson.util import build_spectral_function
+
+a = 1
+natom = 10
+nfrag = 1
+maxiter = 100
+nmom_max_fci = (4,4)
+nmom_max_bath=1
+
+mol = pyscf.gto.Mole()
+mol.atom = ring('H', natom, a)
+mol.basis = 'sto-3g'
+mol.output = 'pyscf.out'
+mol.verbose = 4
+mol.build()
+
+# Hartree-Fock
+mf = pyscf.scf.RHF(mol)
+mf.kernel()
+assert mf.converged
+chempot = (mf.mo_energy[natom//2-1] + mf.mo_energy[natom//2] ) / 2
+gf_hf = Lehmann(mf.mo_energy, np.eye(mf.mo_coeff.shape[0]), chempot=chempot)
+
+# Full system FCI GF
+expr = FCI["1h"](mf)
+th = expr.build_gf_moments(nmom_max_fci[0]) 
+expr = FCI["1p"](mf)
+tp = expr.build_gf_moments(nmom_max_fci[1])
+
+solverh = MBLGF(th, log=NullLogger())
+solverp = MBLGF(tp, log=NullLogger())
+solver = MixedMBLGF(solverh, solverp)
+solver.kernel()
+se = solver.get_self_energy()
+solver = AuxiliaryShift(th[1]+tp[1], se, natom, log=NullLogger())
+solver.kernel()
+static_potential = se.as_static_potential(mf.mo_energy, eta=1e-2)
+gf = solver.get_greens_function()
+dm = gf.occupied().moment(0) * 2.0
+nelec_gf = np.trace(dm)
+print("Exact GF nelec: %s"%nelec_gf)
+
+sc = mf.get_ovlp() @ mf.mo_coeff
+new_fock = sc @ (th[1] + tp[1] + static_potential) @ sc.T
+e, mo_coeff = scipy.linalg.eigh(new_fock, mf.get_ovlp()) 
+chempot = (e[natom//2-1] + e[natom//2] ) / 2
+gf_static = Lehmann(e, np.eye(mf.mo_coeff.shape[0]), chempot=chempot)
+
+gap = lambda gf: gf.physical().virtual().energies[0] - gf.physical().occupied().energies[-1]
+dynamic_gap = gap(gf)
+static_gap = gap(gf_static)
+
+# QP-EwDMET GF
+emb = vayesta.ewf.EWF(mf, solver='FCI', bath_options=dict(bathtype='full', dmet_threshold=1e-12), solver_options=dict(conv_tol=1e-15, n_moments=nmom_max_fci))
+emb.qpewdmet_scmf(proj=1, maxiter=maxiter)
+with emb.site_fragmentation() as f:
+    with f.rotational_symmetry(order=int(natom/nfrag), axis='z') as rot:
+        f.add_atomic_fragment(range(nfrag))
+emb.kernel()
+
+hf_gap = gap(gf_hf)
+emb_dynamic_gap = gap(emb.with_scmf.gf)
+emb_static_gap = gap(emb.with_scmf.gf_qp)
+print("Ran for %s iterations"%emb.with_scmf.iteration)
+print("Hartree-Fock gap: %s"%hf_gap)
+print("Dynamic gap, FCI: %s  Emb: %s"%(dynamic_gap, emb_dynamic_gap))
+print("Static  gap, FCI: %s  Emb: %s"%(static_gap, emb_static_gap))

examples/ewf/molecules/42-fci-incluster-moments.py

@@ -12,16 +12,16 @@
 H  0.0000   0.7572  -0.4692
 H  0.0000  -0.7572  -0.4692
 """
-mol.basis = "cc-pVDZ"
+mol.basis = "sto-6g"
 mol.output = "pyscf.txt"
 mol.build()
 
 # Hartree-Fock
 mf = pyscf.scf.RHF(mol)
 mf.kernel()
 
-# Embedded CCSD
-emb = vayesta.ewf.EWF(mf, bath_options=dict(threshold=1e-6), solver_options=dict(n_moments=(5, 4), solve_lambda=True))
+# Embedded FCI
+emb = vayesta.ewf.EWF(mf, solver='FCI', bath_options=dict(threshold=1e-6), solver_options=dict(n_moments=(5, 4)))
 emb.kernel()
 
 # Reference full system CCSD:

vayesta/core/qemb/qemb.py

@@ -1732,7 +1732,15 @@ def brueckner_scmf(self, *args, **kwargs):
         """Decorator for Brueckner-DMET."""
         self.with_scmf = Brueckner(self, *args, **kwargs)
         self.kernel = self.with_scmf.kernel
-
+    def qpewdmet_scmf(self, *args, **kwargs):
+        """Decorator for QP-EWDMET."""
+        try:
+            from vayesta.core.scmf import QPEWDMET
+        except ImportError:
+            self.log.error("QP-EWDMET requires Dyson installed")
+            return
+        self.with_scmf = QPEWDMET(self, *args, **kwargs)
+        self.kernel = self.with_scmf.kernel
     def check_solver(self, solver):
         is_uhf = np.ndim(self.mo_coeff[1]) == 2
         if self.opts.screening: