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

arXiv:cond-mat/0105003 · Physical review. B, Condensed matter

Phase diagram and optical conductivity of the one-dimensional spinless Holstein model

Q. Wang, H. Zheng, M. Avignon

Published Dec 12, 2000• 14 citations
arXivHTMLPDF

Abstract

The effects of quantum lattice fluctuations on the Peierls transition and the optical conductivity in the one-dimensional Holstein model of spinless fermions have been studied by developing an analytical approach based on the unitary transformation method. We show that when the electron-phonon coupling constant decreases to a finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations. The dimerization gap is much more reduced by the quantum lattice fluctuations than the phonon order parameter. The calculated optical conductivity does not have the inverse-square-root singularity, but it has a peak above the gap edge, and there exists a significant tail below the peak. The peak of optical-conductivity spectrum is not directly corresponding to the dimerized gap. Our results of the phase diagram and the spectral-weight function agree with those of the density-matrix renormalization group and the exact diagonalization methods.

DOI
10.1103/physrevb.63.014305

Related papers

Phase diagram and correlation function of a spin-Peierls system in the ground state: Effects of the quantum lattice fluctuations

Qin Wang, Hang Zheng, Hong Chen

Using a one-dimensional antiferromagnetic Heisenberg chain model with spin-phonon interaction, the effects of quantum lattice fluctuations on the phase diagram and correlation functions in the ground state of the spin-Peierls system are investigated by developing an analytical approach based on the unitary transformation method. To study the nonadiabatic case, the Green's function method is used to implement the perturbation treatment. We show that when the spin-phonon coupling constant decreases or phonon frequency increases, the lattice dimerization and the spin dimerization gap decrease gradually. At some finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations and the system becomes gapless. The inverse-square-root singularity of the density of states at the gap edge in the adiabatic case disappears because of the nonadiabatic effect, which is consistent with the measurement of the optical absorption spectrum in quasi-one-dimensional spin-Peierls systems. The dimerization gap is much more reduced by the quantum lattice fluctuations than the spin dimer order parameter is. This could result in a true spin dimerization gap that is smaller than the activation energy of the optical absorption spectrum.

Physical review. B, Condensed matter•Mar 29, 2002•6 citations

Gapped and gapless ground state of the one-dimensional spinless Holstein model

Hongxing Zheng, M. Avignon

An analytical approach has been developed to study the ground-state phase diagram of a one-dimensional spinless Holstein model and its gapped and gapless phases. We show that when the electron-phonon coupling constant ${g}^{2}/{\ensuremath{\omega}}_{0}$ decreases or the phonon frequency ${\ensuremath{\omega}}_{0}$ increases the lattice dimerization and the gap in the fermionic spectrum decreases gradually. At some critical value ${(g}^{2}/{\ensuremath{\omega}}_{0}{)}_{c}$ or ${\ensuremath{\omega}}_{0c},$ the lattice dimerization disappears and the system becomes gapless Luttinger liquid with phonon-renormalized velocity $v(q)$ and stiffness constant $K(q).$ Our numerical results agree quite well with the results of Monte Carlo simulations.

Physical review. B, Condensed matter•Aug 15, 1998•19 citations

Peierls instability and optical response in the one-dimensional half-filled Holstein model of spinless fermions

Alexander Weiße, Holger Fehske

The effects of quantum lattice fluctuations on the Peierls transition are studied within the one-dimensional Holstein molecular-crystal model by means of exact diagonalization methods. Applying a very efficient variational Lanczos technique, the ground-state phase diagram is obtained in excellent agreement with predictions of recent density matrix renormalization-group calculations. The transition to the charge-density-wave regime is signaled by a strong increase in the charge structure factor. In the metallic regime, the nonuniversal Luttinger liquid parameters (charge velocity and coupling constant) are deduced from a finite-size scaling analysis. The variational results are supported by a complete numerical solution of the quantum phonon Holstein model on small clusters, which is based on a well-controlled phonon Hilbert space truncation procedure. The metallic and charge-density-wave phases are characterized by significant differences in the calculated optical-absorption spectra.

arXiv:cond-mat/9803245•Physical review. B, Condensed matter•Nov 15, 1998•50 citations

Lattice dynamical effects on the Peierls transition in one-dimensional metals and spin chains

Holger Fehske, Michael Holicki, Er Weiße

Summary: The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T = 0) quantum phase transition from a gapless Luttinger-liquid/spin-fluid state to a gapped dimerized phase occurs at a nonzero critical value of the electron/spin-phonon interaction. To study the nature of the spin-Peierls transition at finite temperatures for the infinite system, an alternative Green’s function approach is applied to the magnetostrictive XY model. With increasing phonon frequency the structure factor shows a remarkable crossover from soft-mode to central-peak behaviour. The results are discussed in relation to recent experiments on CuGeO3. 1

•Jan 1, 2000•13 citations

Metal-insulator transition in the one-dimensional Holstein model at half filling

Eric Jeckelmann, Chunli Zhang, Steven R. White

We study the one-dimensional Holstein model with spin-$\frac{1}{2}$ electrons at half filling. Ground-state properties are calculated for long chains with great accuracy using the density-matrix renormalization-group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a nondegenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a twofold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.

arXiv:cond-mat/9903149•Physical review. B, Condensed matter•Sep 15, 1999•102 citations

Dynamical properties of the one-dimensional Holstein model

Chunli Zhang, Eric Jeckelmann, Steven R. White

The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic boundary conditions for three different electron concentrations: a single electron, two electrons of opposite spins, and half filling. A density matrix approach is used to obtain an optimal phonon basis and to truncate the phonon Hilbert space without significant loss of accuracy. This approach allows us to calculate spectral functions for electrons dressed locally by the optimal phonons as well as for bare electrons. We obtain evidence for a smooth crossover from quasifree electrons to a heavy itinerant small polaron (single-electron case) or bipolaron (two-electron case) as the electron-phonon coupling strength increases. At half filling, we observe a crossover from a quasifree-electron ground state to a quasidegenerate Peierls charge-density-wave ground state for a finite electron-phonon coupling. This crossover is marked by an abrupt drop of the Drude weight, which is vanishingly small in the Peierls phase.

arXiv:cond-mat/9812353•Physical review. B, Condensed matter•Nov 15, 1999•76 citations
The effects of quantum lattice fluctuations on the Peierls transition and the optical conductivity in the one-dimensional Holstein model of spinless fermions have been studied by developing an analytical approach based on the unitary transformation method. We show that when the electron-phonon coupling constant decreases to a finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations. The dimerization gap is much more reduced by the quantum lattice fluctuations than the phonon order parameter. The calculated optical conductivity does not have the inverse-square-root singularity, but it has a peak above the gap edge, and there exists a significant tail below the peak. The peak of optical-conductivity spectrum is not directly corresponding to the dimerized gap. Our results of the phase diagram and the spectral-weight function agree with those of the density-matrix renormalization group and the exact diagonalization methods.
Using a one-dimensional antiferromagnetic Heisenberg chain model with spin-phonon interaction, the effects of quantum lattice fluctuations on the phase diagram and correlation functions in the ground state of the spin-Peierls system are investigated by developing an analytical approach based on the unitary transformation method. To study the nonadiabatic case, the Green's function method is used to implement the perturbation treatment. We show that when the spin-phonon coupling constant decreases or phonon frequency increases, the lattice dimerization and the spin dimerization gap decrease gradually. At some finite critical value, the Peierls dimerization is destroyed by the quantum lattice fluctuations and the system becomes gapless. The inverse-square-root singularity of the density of states at the gap edge in the adiabatic case disappears because of the nonadiabatic effect, which is consistent with the measurement of the optical absorption spectrum in quasi-one-dimensional spin-Peierls systems. The dimerization gap is much more reduced by the quantum lattice fluctuations than the spin dimer order parameter is. This could result in a true spin dimerization gap that is smaller than the activation energy of the optical absorption spectrum.
An analytical approach has been developed to study the ground-state phase diagram of a one-dimensional spinless Holstein model and its gapped and gapless phases. We show that when the electron-phonon coupling constant ${g}^{2}/{\ensuremath{\omega}}_{0}$ decreases or the phonon frequency ${\ensuremath{\omega}}_{0}$ increases the lattice dimerization and the gap in the fermionic spectrum decreases gradually. At some critical value ${(g}^{2}/{\ensuremath{\omega}}_{0}{)}_{c}$ or ${\ensuremath{\omega}}_{0c},$ the lattice dimerization disappears and the system becomes gapless Luttinger liquid with phonon-renormalized velocity v(q)v(q)v(q) and stiffness constant K(q).K(q).K(q). Our numerical results agree quite well with the results of Monte Carlo simulations.
The effects of quantum lattice fluctuations on the Peierls transition are studied within the one-dimensional Holstein molecular-crystal model by means of exact diagonalization methods. Applying a very efficient variational Lanczos technique, the ground-state phase diagram is obtained in excellent agreement with predictions of recent density matrix renormalization-group calculations. The transition to the charge-density-wave regime is signaled by a strong increase in the charge structure factor. In the metallic regime, the nonuniversal Luttinger liquid parameters (charge velocity and coupling constant) are deduced from a finite-size scaling analysis. The variational results are supported by a complete numerical solution of the quantum phonon Holstein model on small clusters, which is based on a well-controlled phonon Hilbert space truncation procedure. The metallic and charge-density-wave phases are characterized by significant differences in the calculated optical-absorption spectra.
Summary: The interplay of charge, spin and lattice degrees of freedom is studied for quasi-one-dimensional electron and spin systems coupled to quantum phonons. Special emphasis is put on the influence of the lattice dynamics on the Peierls transition. Using exact diagonalization techniques the ground-state and spectral properties of the Holstein model of spinless fermions and of a frustrated Heisenberg model with magneto-elastic coupling are analyzed on finite chains. In the non-adiabatic regime a (T = 0) quantum phase transition from a gapless Luttinger-liquid/spin-fluid state to a gapped dimerized phase occurs at a nonzero critical value of the electron/spin-phonon interaction. To study the nature of the spin-Peierls transition at finite temperatures for the infinite system, an alternative Green’s function approach is applied to the magnetostrictive XY model. With increasing phonon frequency the structure factor shows a remarkable crossover from soft-mode to central-peak behaviour. The results are discussed in relation to recent experiments on CuGeO3. 1
We study the one-dimensional Holstein model with spin-12\frac{1}{2}21​ electrons at half filling. Ground-state properties are calculated for long chains with great accuracy using the density-matrix renormalization-group method and extrapolated to the thermodynamic limit. We show that for small electron-phonon coupling or large phonon frequency, the insulating Peierls ground state predicted by mean-field theory is destroyed by quantum lattice fluctuations and that the system remains in a metallic phase with a nondegenerate ground state and power-law electronic and phononic correlations. When the electron-phonon coupling becomes large or the phonon frequency small, the system undergoes a transition to an insulating Peierls phase with a twofold degenerate ground state, long-range charge-density-wave order, a dimerized lattice structure, and a gap in the electronic excitation spectrum.
The spectral weight functions and the optical conductivity of the Holstein model are studied on a one-dimensional six-site lattice with periodic boundary conditions for three different electron concentrations: a single electron, two electrons of opposite spins, and half filling. A density matrix approach is used to obtain an optimal phonon basis and to truncate the phonon Hilbert space without significant loss of accuracy. This approach allows us to calculate spectral functions for electrons dressed locally by the optimal phonons as well as for bare electrons. We obtain evidence for a smooth crossover from quasifree electrons to a heavy itinerant small polaron (single-electron case) or bipolaron (two-electron case) as the electron-phonon coupling strength increases. At half filling, we observe a crossover from a quasifree-electron ground state to a quasidegenerate Peierls charge-density-wave ground state for a finite electron-phonon coupling. This crossover is marked by an abrupt drop of the Drude weight, which is vanishingly small in the Peierls phase.