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:0705.1944 · Physical Review B

Polaronic features in the optical properties of the Holstein t−J model

E. Cappelluti, Sergio Ciuchi, S. Fratini

Published Sep 20, 2007• 27 citations
arXivHTMLPDF

Abstract

We derive an exact solution for the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ of one hole in the Holstein $t\text{\ensuremath{-}}J$ model in the framework of dynamical mean-field theory. We investigate the magnetic and phonon features associated with polaron formation as a function of the exchange coupling $J$, electron-phonon interaction $\ensuremath{\lambda}$, and temperature. Our solution directly relates the features of the optical conductivity to excitations in the single-particle spectral function, revealing two distinct mechanisms of closing and filling of the optical pseudogap that take place upon varying the microscopic parameters. We show that the optical absorption at the polaron crossover is characterized by a coexistence of a magnon peak at low frequency and a broad polaronic band at higher frequency. An analytical expression for $\ensuremath{\sigma}(\ensuremath{\omega})$ valid in the polaronic regime is presented.

DOI
10.1103/physrevb.76.125111

Related papers

Polaronic signatures in the optical properties of Nd$_{2-x}$Ce$_x$CuO$_4$

E. Cappelluti, Sergio Ciuchi, S. Fratini

We investigate the temperature and doping dependence of the optical conductivity $σ(ω)$ of Nd$_{2-x}$Ce$_x$CuO$_4$ in terms of magnetic/lattice polaron formation. We employ dynamical mean-field theory in the context of the Holstein-t-J model where an exact analytical solution is available in the limit of infinite connectivity. We show that the pseudogap features in the optical conductivity of this compound can be associated to the formation of lattice polarons assisted by the magnetic interaction.

arXiv:0801.4691•Jan 30, 2008•1 citation

Polarons and Bipolarons in Holstein and Holstein $t-J$ models by Dynamical Mean Field Theory

Sergio Ciuchi, Massimo Capone, E. Cappelluti +1 more

The results of a comparative study of electronic spectral properties as well as phonon Probability Distribution Function (PDF) are reported. The study is done using Dynamical Mean Field Theory for the half-filled spinless and spinful Holstein model and for a single hole in Holstein t-J model. Qualitative changes in phonon PDF signals a polaronic crossover while an electronic Metal Insulator Transition (MIT) due to pairing into a bipolaronic state can be seen from a gap in the electronic DOS or by the vanishing of the quasi particle spectral weight. MIT can be observed only at sufficiently high density provided the Coulomb repulsion is neglected. In the limit of low density the carrier show a polaronic behavior trough the development of a definite polarization shifting the average value of the phonon PDF. At large densities occupied and empty sites result an a bimodal the phonon PDF. At the polaron crossover fluctuation of phonon coordinates tends to be larger than those at any other coupling. In this regime Born-Oppenheimer approximation is shown to fail also when phonon frequency is much less then electron bandwidth. For a single hole in the t-J model a further source of localization is due to magnetic superexchange energy which tends to localize the spin-defect spreading due to the presence of the hole.

arXiv:cond-mat/0510620•Oct 24, 2005•0 citations

Optical absorption and single-particle excitations in the two-dimensional Holstein t−J model

B. Bäuml, Gerhard Wellein, Holger Fehske

To discuss the interplay of electronic and lattice degrees of freedom in systems with strong Coulomb correlations we have performed an extensive numerical study of the two-dimensional Holstein $t\ensuremath{-}J$ model. The model describes the interaction of holes, doped in a quantum antiferromagnet, with a dispersionsless optical phonon mode. We apply finite-lattice Lanczos diagonalization, combined with a well-controlled phonon Hilbert space truncation, to the Hamiltonian. The focus is on the dynamical properties. In particular we have evaluated the single-particle spectral function and the optical conductivity for characteristic hole-phonon couplings, spin exchange interactions, and phonon frequencies. The results are used to analyze the formation of lattice hole polarons in great detail. Links with experiments on layered perovskites are made. In addition, we compare the Chebyshev recursion and maximum entropy algorithms, used for calculating spectral functions, with standard Lanczos methods.

arXiv:cond-mat/9802181•Physical review. B, Condensed matter•Aug 15, 1998•76 citations

Calculation of excited polaron states in the Holstein model

O. S. Barišić

An exact-diagonalization technique is used to investigate the low-lying excited polaron states in the Holstein model for the infinite one-dimensional lattice. For moderate values of the adiabatic ratio, a comprehensive picture, involving three excited (coherent) polaron bands below the phonon threshold, is obtained. The coherent contribution of the excited states to both the single-electron spectral density and the optical conductivity is evaluated and, due to the invariance of the Hamiltonian under the space inversion, the two are shown to contain complementary information about the single-electron system at zero temperature. The chosen method reveals the connection between the excited bands and the renormalized local phonon excitations of the adiabatic theory, as well as the regime of parameters for which the electron self-energy has notable nonlocal contributions. Finally, it is shown that the hybridization of two polaron states allows a simple description of the ground and first excited states in the crossover regime.

arXiv:cond-mat/0211189•Physical Review B•Feb 12, 2004•40 citations

Optical conductivity of polaronic charge carriers

Jan Loos, Martin Hohenadler, Andreas Alvermann +1 more

The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalization yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis is put on deviations from weak-coupling, small-polaron or one-electron theories occurring at intermediate coupling and/or finite carrier density. The analytical results are in surprisingly good agreement with exact data, and exhibit the characteristic polaronic excitations observed in experiments on manganites.

arXiv:cond-mat/0703611•Journal of Physics Condensed Matter•May 17, 2007•13 citations

Dynamic properties of a polaron coupled to dispersive optical phonons

J. Bonča, S. A. Trugman

We study static and dynamic properties of an electron coupled to dispersive quantum optical phonons in the framework of the Holstein model defined on a one-dimensional lattice. Calculations are performed using the Lanczos algorithm based on a highly efficient construction of the variational Hilbert space. Even small phonon dispersion has a profound effect on the low-energy optical response. While the upward phonon dispersion broadens the optical spectra due to single-phonon excitations, the downward dispersion has the opposite effect. With increasing dispersion, a multiphonon excitation (MPE) state becomes the lowest excited state of the system at zero momentum and determines the low-frequency response of the optical conductivity where the threshold for optical absorption moves below the single-phonon frequency. Multiphonon states form a well-defined bandlike feature just above the polaron band as clearly seen in the electron spectral function. Low-energy MPEs should be observable in systems with strong optical phonon dispersion in optical as well as angle-resolved photoemission experiments.

Physical review. B./Physical review. B•Feb 12, 2021•28 citations
We derive an exact solution for the optical conductivity \ensuremathσ(\ensuremathω)\ensuremath{\sigma}(\ensuremath{\omega})\ensuremathσ(\ensuremathω) of one hole in the Holstein t\ensuremath-Jt\text{\ensuremath{-}}Jt\ensuremath-J model in the framework of dynamical mean-field theory. We investigate the magnetic and phonon features associated with polaron formation as a function of the exchange coupling JJJ, electron-phonon interaction \ensuremathλ\ensuremath{\lambda}\ensuremathλ, and temperature. Our solution directly relates the features of the optical conductivity to excitations in the single-particle spectral function, revealing two distinct mechanisms of closing and filling of the optical pseudogap that take place upon varying the microscopic parameters. We show that the optical absorption at the polaron crossover is characterized by a coexistence of a magnon peak at low frequency and a broad polaronic band at higher frequency. An analytical expression for \ensuremathσ(\ensuremathω)\ensuremath{\sigma}(\ensuremath{\omega})\ensuremathσ(\ensuremathω) valid in the polaronic regime is presented.
Polaronic signatures in the optical properties of Nd2−x_{2-x}2−x​Cex_xx​CuO4_44​
We investigate the temperature and doping dependence of the optical conductivity σ(ω)σ(ω)σ(ω) of Nd2−x_{2-x}2−x​Cex_xx​CuO4_44​ in terms of magnetic/lattice polaron formation. We employ dynamical mean-field theory in the context of the Holstein-t-J model where an exact analytical solution is available in the limit of infinite connectivity. We show that the pseudogap features in the optical conductivity of this compound can be associated to the formation of lattice polarons assisted by the magnetic interaction.
Polarons and Bipolarons in Holstein and Holstein t−Jt-Jt−J models by Dynamical Mean Field Theory
The results of a comparative study of electronic spectral properties as well as phonon Probability Distribution Function (PDF) are reported. The study is done using Dynamical Mean Field Theory for the half-filled spinless and spinful Holstein model and for a single hole in Holstein t-J model. Qualitative changes in phonon PDF signals a polaronic crossover while an electronic Metal Insulator Transition (MIT) due to pairing into a bipolaronic state can be seen from a gap in the electronic DOS or by the vanishing of the quasi particle spectral weight. MIT can be observed only at sufficiently high density provided the Coulomb repulsion is neglected. In the limit of low density the carrier show a polaronic behavior trough the development of a definite polarization shifting the average value of the phonon PDF. At large densities occupied and empty sites result an a bimodal the phonon PDF. At the polaron crossover fluctuation of phonon coordinates tends to be larger than those at any other coupling. In this regime Born-Oppenheimer approximation is shown to fail also when phonon frequency is much less then electron bandwidth. For a single hole in the t-J model a further source of localization is due to magnetic superexchange energy which tends to localize the spin-defect spreading due to the presence of the hole.
To discuss the interplay of electronic and lattice degrees of freedom in systems with strong Coulomb correlations we have performed an extensive numerical study of the two-dimensional Holstein $t\ensuremath{-}J$ model. The model describes the interaction of holes, doped in a quantum antiferromagnet, with a dispersionsless optical phonon mode. We apply finite-lattice Lanczos diagonalization, combined with a well-controlled phonon Hilbert space truncation, to the Hamiltonian. The focus is on the dynamical properties. In particular we have evaluated the single-particle spectral function and the optical conductivity for characteristic hole-phonon couplings, spin exchange interactions, and phonon frequencies. The results are used to analyze the formation of lattice hole polarons in great detail. Links with experiments on layered perovskites are made. In addition, we compare the Chebyshev recursion and maximum entropy algorithms, used for calculating spectral functions, with standard Lanczos methods.
An exact-diagonalization technique is used to investigate the low-lying excited polaron states in the Holstein model for the infinite one-dimensional lattice. For moderate values of the adiabatic ratio, a comprehensive picture, involving three excited (coherent) polaron bands below the phonon threshold, is obtained. The coherent contribution of the excited states to both the single-electron spectral density and the optical conductivity is evaluated and, due to the invariance of the Hamiltonian under the space inversion, the two are shown to contain complementary information about the single-electron system at zero temperature. The chosen method reveals the connection between the excited bands and the renormalized local phonon excitations of the adiabatic theory, as well as the regime of parameters for which the electron self-energy has notable nonlocal contributions. Finally, it is shown that the hybridization of two polaron states allows a simple description of the ground and first excited states in the crossover regime.
The optical conductivity of charge carriers coupled to quantum phonons is studied in the framework of the one-dimensional spinless Holstein model. For one electron, variational diagonalization yields exact results in the thermodynamic limit, whereas at finite carrier density analytical approximations based on previous work on single-particle spectral functions are obtained. Particular emphasis is put on deviations from weak-coupling, small-polaron or one-electron theories occurring at intermediate coupling and/or finite carrier density. The analytical results are in surprisingly good agreement with exact data, and exhibit the characteristic polaronic excitations observed in experiments on manganites.
We study static and dynamic properties of an electron coupled to dispersive quantum optical phonons in the framework of the Holstein model defined on a one-dimensional lattice. Calculations are performed using the Lanczos algorithm based on a highly efficient construction of the variational Hilbert space. Even small phonon dispersion has a profound effect on the low-energy optical response. While the upward phonon dispersion broadens the optical spectra due to single-phonon excitations, the downward dispersion has the opposite effect. With increasing dispersion, a multiphonon excitation (MPE) state becomes the lowest excited state of the system at zero momentum and determines the low-frequency response of the optical conductivity where the threshold for optical absorption moves below the single-phonon frequency. Multiphonon states form a well-defined bandlike feature just above the polaron band as clearly seen in the electron spectral function. Low-energy MPEs should be observable in systems with strong optical phonon dispersion in optical as well as angle-resolved photoemission experiments.