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

Communications in Theoretical Physics

Nonlinear Lattice Effect on Ground State of One-Dimensional Electron-Phonon System

Zhou Guang-Hui, Han Ding-An

Published Jan 15, 2003• 0 citations
Publisher

Abstract

We study the nonlinear lattice effect on the ground state in a one-dimensional spinless Holstein model with nonadiabitical coupling and squeezing by means of the parameter variational approach. Our results show that the introduction of a hard quartic term in the lattice potential increases the ground state energy of the system when electron-phonon coupling is strong, and the increment is sensitive to the magnitude of the lattice quartic force constant. In this case the nonlinear lattice effects should be taken into account to describe satisfactorily some physical properties of the coupling system.

DOI
10.1088/0253-6102/39/1/101

Related papers

Exact solution for the ground-state energy band of an extended one-dimensional Holstein model

Feng Pan, L. R. Dai, Jerry Paul Draayer

We demonstrate that the ground-state energy band of an extended one-dimensional Holstein model, featuring a specific type of nonlinear electron-phonon coupling for a single electron in the band, is exactly solvable. Numerical results indicate that, despite the significant differences in electron-phonon coupling between the extended Holstein model and the original Holstein model, the ground-state energy of the Holstein model can be accurately reproduced by the extended model through appropriate rescaling of the coupling parameter. Additionally, for an $N$-site lattice, there are ${2}^{N\ensuremath{-}1}$ distinct choices for the set of parameters in the nonlinear electron-phonon coupling, all yielding the same ground-state energy but with varying ground-state properties. This flexibility allows for the selection of the optimal parameter set in the extended model to best simulate the ground-state properties of the system.

Physical review. B./Physical review. B•Nov 13, 2024•2 citations

The Stabilities of the Ground State and the Polaron Arising from the Squeezing ? Antisqueezing Effect in Strongly Coupled Electron ? Phonon Systems

Pang Xiao‐feng

The influences of the squeezing–antisqueezing effect arising from variations of the electron density and motion of polarons and nonadiabatic phonon fluctuations on the properties of the ground state and the binding energy of the polaron in the Holstein model of coupled one-dimensional electron–phonon systems with spin 1/2 in the cases of high and low electron densities have been studied by using the Bogolyubov transformation and a new ansatz for states that includes correlation effects among the one-phonon coherent and two-phonon squeezed and polaronic states. The results obtained show that the squeezing–antisqueezing (correlation) effect results in that the ground state energy of the systems is significantly lowered, and the binding energy of the polaron is considerably increased. Thus, the stability of the systems and of the polaron are obviously enhanced in such a case when compared with the uncorrelated case. This shows that the ground state determined by the new state ansatz is most stable, and the new ansatz introduced here is very relevant for the coupled electron–phonon systems, especially in strongly coupled and largely squeezed cases.

physica status solidi (b)•Feb 1, 2000•3 citations

The properties of the ground state of the nonadiabatically coupled electron-phonon systems with correlated displacement and squeezing

Pang Xiao‐feng, Ping Li

Effects of the nonadiabatic phonon fluctuations on the ground state of coupled one-dimensional electron-phonon systems with high and low electron-densities were investigated by a new ansatz including correlated interaction of the displacement and squeezing. The correlated effect resulted in noticeable reduction of ground state energy of the systems, and obvious increases of binding energy of the polarons occurred. Thus, the stabilities of the polaron and of the systems were significantly enhanced, exactly steady ground state of the Holstein model, then, was obtained by the new ansatz for the coupled electron-phonon systems. In general, the new ansatz were found to be very relevant for the strong coupling and large squeezing cases in nonadiabatically coupled electron-photon systems.

Acta Physica Sinica (Overseas Edition)•Aug 1, 1999•0 citations

CHANGES IN THE PHYSICAL PROPERTIES OF NONADIABATICALLY COUPLED ELECTRON–PHONON SYSTEMS ARISING FROM SQUEEZING–ANTISQUEEZING EFFECT

Pang Xiao‐feng

Changes in the physical properties such as the ground state properties, charge density wave ordering, binding energy and energy bandwidth of polaron and quantum fluctuation, and minimum uncertainty relation of phonons and nonadiabatically coupled electron–phonon systems with spin-1/2 have been investigated by our new state ansatz which can account for correlation among the phononic displacement, squeezing and polaron effects using variational method in one-dimensional Holstein model. The investigation here shows that the squeezing–antisqueezing effect (correlated) results in a decrease of the ground state energy, an increase of the binding energy of polarons, the reduction of the uncertainty and quantum fluctuation of the phonons, a decrease of polaron narrowing of electron bandwidth, an increase of tunneling effect of the polarons and an increase of CDW ordering and phonon staggered ordering when compared with the uncorrelated case. Therefore, this shows that the ground state determined by the new state ansatz is the most stable. The new ansatz which include the squeezing–antisqueezing (correlated) effect is very relevant for the coupled electron–phonon systems, especially in strongly coupled and highly squeezed cases.

International Journal of Modern Physics B•Dec 30, 2003•0 citations

Correlated squeezed polaron states in one dimension

Chi‐Fai Lo, Roger Sollie

In this paper we have applied the correlated squeezed-state approach to investigate the ground-state properties of the one-dimensional Hubbard model with a local Holstein-type electron-phonon interaction. We have introduced a variational ground state in which the phonon subsystem is in a correlated squeezed state. The correlated squeezed state has built in the correlation between different phonon modes induced by the linear coupling with the electrons. With optimal values of the variational parameters the correlated squeezed state will by construction yield an energy lower than those obtained in earlier treatments. This means that our variational ansatz is more stable as the ground state of the system. Furthermore, our variational study shows that in the correlated squeezed state the polaronic reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is considerably weakened. This weakening of the reduction effect should, in turn, affect other physical properties of the system.

Physical review. B, Condensed matter•Oct 1, 1993•18 citations

Properties of ground state and anomalous quantum fluctuations in one-dimensional polaron—soliton systems—the effects of electron-two-phonon interaction and non-adiabatic quantum correlations

罗质华, 曹锡金, 余超凡

Based on the Holstein model Hamiltonian of one-dimensional molecular crystals, by making use of the expansion approach of the correlated squeezed-coherent states of phonon instead of the two-phonon coherent state expansion scheme, the properties of the ground state and the anomalous quantum fluctuations are investigated in a strongly coupled electron—phonon system with special consideration of the electron-two-phonon interaction. The effective renormalization ( i ) of the displacement of the squeezed phonons with the effect of the squeezed-coherent states of phonon and both the electron-displaced phonon and the polaron-squeezed phonon correlations have been combined to obtain the anomalous quantum fluctuations for the corrections of the coherent state. Due to these non-adiabatic correlations, the effective displacement parameter i is larger than the ordinary parameter α i (0) . In comparison with the electron-one-phonon interaction ( g ) corrected as i g , we have found the electron-two-phonon interaction ( g 1 ) corrected as i 2 g 1 is enhanced significantly. For this reason, the ground state energy ( E 0 (2) ) contributed by the electron-two-phonon interaction is more negative than the single-phonon case ( E 0 (1) ) and the soliton solution is more stable. At the same time, the effects of the electron-two-phonon interaction greatly increase the polaron energy and the quantum fluctuations. Furthermore, in a deeper level, we have considered the effect of the polaron-squeezed phonon correlation ( f -correlation). Since this correlation parameter f > 1, this effect will strengthen the electron-one and two-phonon interactions by f i g and f 2 i 2 g 1 , respectively. The final results show that the ground state energy and the polaron energy will appear more negative further and the quantum fluctuations will gain further improvement.

Chinese Physics B•Jun 1, 2011•3 citations
We study the nonlinear lattice effect on the ground state in a one-dimensional spinless Holstein model with nonadiabitical coupling and squeezing by means of the parameter variational approach. Our results show that the introduction of a hard quartic term in the lattice potential increases the ground state energy of the system when electron-phonon coupling is strong, and the increment is sensitive to the magnitude of the lattice quartic force constant. In this case the nonlinear lattice effects should be taken into account to describe satisfactorily some physical properties of the coupling system.
We demonstrate that the ground-state energy band of an extended one-dimensional Holstein model, featuring a specific type of nonlinear electron-phonon coupling for a single electron in the band, is exactly solvable. Numerical results indicate that, despite the significant differences in electron-phonon coupling between the extended Holstein model and the original Holstein model, the ground-state energy of the Holstein model can be accurately reproduced by the extended model through appropriate rescaling of the coupling parameter. Additionally, for an NNN-site lattice, there are ${2}^{N\ensuremath{-}1}$ distinct choices for the set of parameters in the nonlinear electron-phonon coupling, all yielding the same ground-state energy but with varying ground-state properties. This flexibility allows for the selection of the optimal parameter set in the extended model to best simulate the ground-state properties of the system.
The influences of the squeezing–antisqueezing effect arising from variations of the electron density and motion of polarons and nonadiabatic phonon fluctuations on the properties of the ground state and the binding energy of the polaron in the Holstein model of coupled one-dimensional electron–phonon systems with spin 1/2 in the cases of high and low electron densities have been studied by using the Bogolyubov transformation and a new ansatz for states that includes correlation effects among the one-phonon coherent and two-phonon squeezed and polaronic states. The results obtained show that the squeezing–antisqueezing (correlation) effect results in that the ground state energy of the systems is significantly lowered, and the binding energy of the polaron is considerably increased. Thus, the stability of the systems and of the polaron are obviously enhanced in such a case when compared with the uncorrelated case. This shows that the ground state determined by the new state ansatz is most stable, and the new ansatz introduced here is very relevant for the coupled electron–phonon systems, especially in strongly coupled and largely squeezed cases.
Effects of the nonadiabatic phonon fluctuations on the ground state of coupled one-dimensional electron-phonon systems with high and low electron-densities were investigated by a new ansatz including correlated interaction of the displacement and squeezing. The correlated effect resulted in noticeable reduction of ground state energy of the systems, and obvious increases of binding energy of the polarons occurred. Thus, the stabilities of the polaron and of the systems were significantly enhanced, exactly steady ground state of the Holstein model, then, was obtained by the new ansatz for the coupled electron-phonon systems. In general, the new ansatz were found to be very relevant for the strong coupling and large squeezing cases in nonadiabatically coupled electron-photon systems.
Changes in the physical properties such as the ground state properties, charge density wave ordering, binding energy and energy bandwidth of polaron and quantum fluctuation, and minimum uncertainty relation of phonons and nonadiabatically coupled electron–phonon systems with spin-1/2 have been investigated by our new state ansatz which can account for correlation among the phononic displacement, squeezing and polaron effects using variational method in one-dimensional Holstein model. The investigation here shows that the squeezing–antisqueezing effect (correlated) results in a decrease of the ground state energy, an increase of the binding energy of polarons, the reduction of the uncertainty and quantum fluctuation of the phonons, a decrease of polaron narrowing of electron bandwidth, an increase of tunneling effect of the polarons and an increase of CDW ordering and phonon staggered ordering when compared with the uncorrelated case. Therefore, this shows that the ground state determined by the new state ansatz is the most stable. The new ansatz which include the squeezing–antisqueezing (correlated) effect is very relevant for the coupled electron–phonon systems, especially in strongly coupled and highly squeezed cases.
In this paper we have applied the correlated squeezed-state approach to investigate the ground-state properties of the one-dimensional Hubbard model with a local Holstein-type electron-phonon interaction. We have introduced a variational ground state in which the phonon subsystem is in a correlated squeezed state. The correlated squeezed state has built in the correlation between different phonon modes induced by the linear coupling with the electrons. With optimal values of the variational parameters the correlated squeezed state will by construction yield an energy lower than those obtained in earlier treatments. This means that our variational ansatz is more stable as the ground state of the system. Furthermore, our variational study shows that in the correlated squeezed state the polaronic reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is considerably weakened. This weakening of the reduction effect should, in turn, affect other physical properties of the system.
Based on the Holstein model Hamiltonian of one-dimensional molecular crystals, by making use of the expansion approach of the correlated squeezed-coherent states of phonon instead of the two-phonon coherent state expansion scheme, the properties of the ground state and the anomalous quantum fluctuations are investigated in a strongly coupled electron—phonon system with special consideration of the electron-two-phonon interaction. The effective renormalization ( i ) of the displacement of the squeezed phonons with the effect of the squeezed-coherent states of phonon and both the electron-displaced phonon and the polaron-squeezed phonon correlations have been combined to obtain the anomalous quantum fluctuations for the corrections of the coherent state. Due to these non-adiabatic correlations, the effective displacement parameter i is larger than the ordinary parameter α i (0) . In comparison with the electron-one-phonon interaction ( g ) corrected as i g , we have found the electron-two-phonon interaction ( g 1 ) corrected as i 2 g 1 is enhanced significantly. For this reason, the ground state energy ( E 0 (2) ) contributed by the electron-two-phonon interaction is more negative than the single-phonon case ( E 0 (1) ) and the soliton solution is more stable. At the same time, the effects of the electron-two-phonon interaction greatly increase the polaron energy and the quantum fluctuations. Furthermore, in a deeper level, we have considered the effect of the polaron-squeezed phonon correlation ( f -correlation). Since this correlation parameter f > 1, this effect will strengthen the electron-one and two-phonon interactions by f i g and f 2 i 2 g 1 , respectively. The final results show that the ground state energy and the polaron energy will appear more negative further and the quantum fluctuations will gain further improvement.