Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

International Journal of Modern Physics B

A CONCISE APPROACH FOR ONE-DIMENSIONAL HOLSTEIN MODEL

Qing-Bao Ren, Qing‐Hu Chen

Published Sep 30, 2007• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0217979207045451

Related papers

Holstein polaron

J. Bonča, S. A. Trugman, I. Batistić

We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest computational resources (12-digit accuracy for the one-dimensional polaron energy at intermediate coupling). We compute ground-state and low-lying excited-state properties of the model at continuous values of the wave vector k in essentially all parameter regimes. Our results for the polaron energy band, effective mass, and correlation functions compare favorably with those of other numerical techniques, including the density-matrix renormalization-group technique, the global-local method, and the exact diagonalization technique. We find a phase transition for the first excited state between a bound and unbound system of a polaron and an additional phonon excitation. The phase transition is also treated in strong-coupling perturbation theory.

arXiv:cond-mat/9812252•Physical review. B, Condensed matter•Jul 15, 1999•281 citations

Two-Site Holstein Model: a Variational Wavefunction Analysis

Qing-Bao Ren, Qing‐Hu Chen

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.

Chinese Physics Letters•Oct 27, 2005•6 citations

A New Variational Study for Two-Site Holstein Model

Qing-Bao Ren, Qing‐Hu Chen

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.

Communications in Theoretical Physics•Feb 1, 2005•3 citations

A New Variational Study for Two-Site Holstein Model

RENQing-Bao, CHENQing-Hu

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.

理论物理通讯：英文版•Jan 1, 2005•0 citations

Ground-state properties of the Holstein model near the adiabatic limit

Zhou Li, Devin Baillie, C. Blois +1 more

We adapt a variational procedure to calculate ground-state properties of the Holstein model in the adiabatic limit. At strong coupling, this adaption leads to rapid convergence of results. The intermediate coupling regime is further handled with an adaptive algorithm. We also use semiclassically derived results for the adiabatic end point, along with weak coupling perturbation theory. These establish weak and strong coupling (or large and small polaron, respectively) regimes in two dimensions or higher. As is well known, these are connected smoothly, but the crossover becomes increasingly abrupt as the phonon frequency decreases.

arXiv:1003.1952•Physical Review B•Mar 9, 2010•34 citations

Variational study of the discrete Holstein model

A. La Magna, R. Pucci

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.

Physical review. B, Condensed matter•Apr 1, 1996•42 citations
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.
We describe a variational method to solve the Holstein model for an electron coupled to dynamical, quantum phonons on an infinite lattice. The variational space can be systematically expanded to achieve high accuracy with modest computational resources (12-digit accuracy for the one-dimensional polaron energy at intermediate coupling). We compute ground-state and low-lying excited-state properties of the model at continuous values of the wave vector k in essentially all parameter regimes. Our results for the polaron energy band, effective mass, and correlation functions compare favorably with those of other numerical techniques, including the density-matrix renormalization-group technique, the global-local method, and the exact diagonalization technique. We find a phase transition for the first excited state between a bound and unbound system of a polaron and an additional phonon excitation. The phase transition is also treated in strong-coupling perturbation theory.
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.
We adapt a variational procedure to calculate ground-state properties of the Holstein model in the adiabatic limit. At strong coupling, this adaption leads to rapid convergence of results. The intermediate coupling regime is further handled with an adaptive algorithm. We also use semiclassically derived results for the adiabatic end point, along with weak coupling perturbation theory. These establish weak and strong coupling (or large and small polaron, respectively) regimes in two dimensions or higher. As is well known, these are connected smoothly, but the crossover becomes increasingly abrupt as the phonon frequency decreases.
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.