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Chinese Physics Letters

Two-Site Holstein Model: a Variational Wavefunction Analysis

Qing-Bao Ren, Qing‐Hu Chen

Published Oct 27, 2005• 6 citations
Publisher

Abstract

A novel variational approach is proposed to calculate the ground-state (GS) properties of the two-site Holstein model. By the linear superposition of two coherent states, which simulate the behaviour of the weak and strong coupling limits, we can obtain very accurate GS energy for arbitrary electron–phonon coupling constant. Other GS properties are also discussed. Moreover, the present concise approach is hopefully generalized to many other Holstein models.

DOI
10.1088/0256-307x/22/11/052

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A novel variational approach is proposed to calculate the ground-state (GS) properties of the two-site Holstein model. By the linear superposition of two coherent states, which simulate the behaviour of the weak and strong coupling limits, we can obtain very accurate GS energy for arbitrary electron–phonon coupling constant. Other GS properties are also discussed. Moreover, the present concise approach is hopefully generalized to many other Holstein models.
A variational approach is developed to study the groundstate (GS) of the two-site Holstein model. By the extended coherent state, where the more phonon correlations are easily incorporated, we can get the very accurate ground state energy for all electron-phonon coupling range in typical values of hopping integral t = 0.5,1.1, and 2.1 (in units of phonon frequency ω 0 ), which covers the crossover region from antiadiabatic limit to the adiabatic limit. Within a very wide t range [0,2.7], the exact results for the GS energy are obtained with the twelfth (fourteenth) order corrections to the zeroth order wave function. Moreover, the present approach is more concise than any other analytical ones in this field, and hopefully can be easily generalized to many other Holstein models.
A variational approach is developed to study the groundstate (GS) of the two-site Holstein model. By the extended coherent state, where the more phonon correlations are easily incorporated, we can get the very accurate ground state energy for all electron-phonon coupling range in typical values of hopping integral t = 0.5, 1.1, and 2.1 (in units of phonon frequency ωo ), which covers the crossover region from antiadiabatic limit to the adiabatic limit. Within a very wide t range [0, 2.7], the exact results for the GS energy are obtained with the twelfth (fourteenth) order corrections to the zeroth order wave function. Moreover, the present approach is more concise than any other analytical ones in this field, and hopefully can be easily generalized to many other Holstein models.
A concise variational approach is to propose to calculate the ground-state properties of none-dimensional Holstein model. The results in the weak and strong coupling limit can be easily recovered analytically. It is shown that, in the nontrivial intermediate electron-phonon coupling regime, the present results are in good agreement with those by density-matrix renormalization group and numerical exact diagonalizations. The present approach is more concise than any other analytical ones in this field, and can be easily generalized to Holstein models in higher dimensions and with more electrons.
The Holstein model for the interaction between one particle and a large (\ensuremath{\sim}100 sites) chain of oscillators has been treated through a numerical self-consistent procedure. The adopted variational state is a generalization of the most commonly used trial wave functions and the results are correct both in the weak and the strong-coupling limits. The comparison of our variational ground-state energy with the exact calculations on small clusters also supports the validity of the approach. Moreover, all the relevant physical quantities are analytical functions of the parameters. The appearance of a self-trapped state is discussed critically in connection with the changes of the dynamical condition of the system. The role of the quantum fluctuations of the lattice in the intermediate-coupling regime is emphasized by calculating the phonons wave functions. The application of the results to some physical systems is presented in the conclusion. \textcopyright{} 1996 The American Physical Society.
A variational technique is developed to investigate the polaronic features of the Holstein molecular-crystal model. It is based on a linear superposition of Bloch states that describe large and small polaron wave functions. It is shown that this method provides a very good description of the regime characterized by intermediate values of the electron-phonon coupling constant (the so-called intermediate polaron) for any value of the adiabatic parameter ${\ensuremath{\omega}}_{0}/t.$ The polaron ground state energy in one and two dimensions is calculated and successfully compared with the best estimates available providing a clear physical interpretation of the intermediate polaron. The band structure, the spectral weight of the ground state and the lattice displacement associated to the polaron are also calculated and discussed. The method has the advantage of requiring very little computational effort.
The two-site Holstein model is studied by the analytical method of the coherent-state expansion. We obtain the recursive relationship among the expansion coefficients, which leads to the exact solutions of the eigenstate properties. The exact ground-state results in the whole coupling strength region and from antiadiabatic to adiabatic limits are in perfect agreement with that available by the exact numerical diagonalization technique. Comparison with the best perturbation results shows the success and shortcoming of the perturbative method. The coherent-state expansion method is a promising approach in studying electron-phonon $(e\ensuremath{-}\mathrm{ph})$ coupling systems.