An efficient, yet very accurate trial wave function, constructed from projecting the well-known Davydov D1 Ansatz onto momentum eigenstates, is employed to study the ground state properties of the generalized Holstein Hamiltonian with simultaneous diagonal and off-diagonal coupling. Ground-state energies have been obtained with a precision matching that of the computationally much more demanding density-matrix renormalization group method. The delocalized D1 Ansatz lowers the ground-state energies at the Brillouin zone boundary significantly compared with the Toyozawa and Global-Local Ansätze in the weak coupling regime, while considerable improvement is demonstrated to have been achieved over the entire Brillouin zone in the strong coupling regime. Unique solutions are obtained with the delocalized D1 for different initial conditions when the transfer integral is 20 times the phonon frequency at the zone center, implying the absence of any self-trapping discontinuity. The scaled correlation variance is found to fit satisfactorily well with the predictions of the perturbation theories.An efficient, yet very accurate trial wave function, constructed from projecting the well-known Davydov D1 Ansatz onto momentum eigenstates, is employed to study the ground state properties of the generalized Holstein Hamiltonian with simultaneous diagonal and off-diagonal coupling. Ground-state energies have been obtained with a precision matching that of the computationally much more demanding density-matrix renormalization group method. The delocalized D1 Ansatz lowers the ground-state energies at the Brillouin zone boundary significantly compared with the Toyozawa and Global-Local Ansätze in the weak coupling regime, while considerable improvement is demonstrated to have been achieved over the entire Brillouin zone in the strong coupling regime. Unique solutions are obtained with the delocalized D1 for different initial conditions when the transfer integral is 20 times the phonon frequency at the zone center, implying the absence of any self-trapping discontinuity. The scaled correlation variance is found to fit satisfactorily well with the predictions of the perturbation theories.

The Journal of Chemical PhysicsMay 7, 201323 citations

Formation and local symmetry of the Holstein polaron in thet–Jmodel

Han Ma, T K Lee, Yan Chen

The formation and local symmetry of a spin–lattice polaron has been investigated semiclassically in planar Holstein t – J -like models within the exact diagonalization method. Due to the interplay of strong correlations and electron–lattice interaction, the doped hole may either move freely or lead to the localized spin–lattice distortion and form a Holstein polaron. The formation of a polaron breaks the translational symmetry by suppression of antiferromagnetic correlations and inducement of ferromagnetic correlations locally. Moreover, the breaking of local rotational symmetry around the polaron has been shown. The ground state is generically a parity singlet and the first excited state may be a parity doublet. Further consequences of the density of states spectra for comparison with scanning tunneling microscopy experiments are discussed.The formation and local symmetry of a spin–lattice polaron has been investigated semiclassically in planar Holstein t – J -like models within the exact diagonalization method. Due to the interplay of strong correlations and electron–lattice interaction, the doped hole may either move freely or lead to the localized spin–lattice distortion and form a Holstein polaron. The formation of a polaron breaks the translational symmetry by suppression of antiferromagnetic correlations and inducement of ferromagnetic correlations locally. Moreover, the breaking of local rotational symmetry around the polaron has been shown. The ground state is generically a parity singlet and the first excited state may be a parity doublet. Further consequences of the density of states spectra for comparison with scanning tunneling microscopy experiments are discussed.

arXiv:1212.0699New Journal of PhysicsApr 26, 20132 citations

Quantum mechanical Hamiltonians with large ground-state degeneracy

Choonkyu Lee, Kimyeong Lee

arXiv:1211.5211Annals of PhysicsJan 11, 20130 citations

Instability of tunneling and the concept of molecular structure in quantum mechanics: The case of pyramidal molecules and the enantiomer problem

P. Claverie, Giovanni Jona-Lasinio

In this paper we propose a possible explanation of the fact that certain molecules exhibiting symmetric configurations are localized in one of them, instead of being delocalized as predicted by a naive application of quantum mechanics. Our mechanism is based upon the instability, in the semiclassical regime, of delocalized states under small perturbations (among which we consider the reaction field due to the environment). This mechanism predicts, for example, a different behavior for ${\mathrm{NH}}_{3}$ and ${\mathrm{AsH}}_{3}$ (delocalized ground state in the former case, localized ground state in the latter case), and similar to the case of ${\mathrm{AsH}}_{3}$ we expect localized states in the case of optical isomers, in agreement with the empirical evidence. Possible consequences concerning the understanding of the ``classical limit'' in general are briefly outlined.In this paper we propose a possible explanation of the fact that certain molecules exhibiting symmetric configurations are localized in one of them, instead of being delocalized as predicted by a naive application of quantum mechanics. Our mechanism is based upon the instability, in the semiclassical regime, of delocalized states under small perturbations (among which we consider the reaction field due to the environment). This mechanism predicts, for example, a different behavior for ${\mathrm{NH}}_{3}$ and ${\mathrm{AsH}}_{3}$ (delocalized ground state in the former case, localized ground state in the latter case), and similar to the case of ${\mathrm{AsH}}_{3}$ we expect localized states in the case of optical isomers, in agreement with the empirical evidence. Possible consequences concerning the understanding of the ``classical limit'' in general are briefly outlined.

Physical Review AApr 1, 198690 citations

{\mathrm{NH}}_{3}

and

{\mathrm{AsH}}_{3}

(delocalized ground state in the former case, localized ground state in the latter case), and similar to the case of

{\mathrm{AsH}}_{3}

we expect localized states in the case of optical isomers, in agreement with the empirical evidence. Possible consequences concerning the understanding of the ``classical limit'' in general are briefly outlined.