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

AIP conference proceedings

Strong correlations in the two-dimensional extended Holstein-Hubbard model

I. V. Sankar, Ashok Chatterjee

Published Jan 1, 2013• 1 citation
Publisher

Abstract

The Holstein-Hubbard model is studied in two dimensions to explore the nature of polarons as a function of hole concentration in the strong correlation regime. A series of canonical transformations is performed to obtain an effective extended Hubbard model which, in the strong on-site electron-electron correlation regime, transforms into a t-J model and is solved using the mean-field Hartree-Fock approximation (HFA). It is shown that the hopping parameter which is related to the bandwidth of the polaron is very small for low (x ≈ 0) and high (x ≈ 1) hole concentrations whereas the hopping parameter is much larger for the intermediate hole concentrations.

DOI
10.1063/1.4791448

Related papers

Effect of the hole concentration on the polaronic mobility for the strongly interacting electrons

Debika Debnath, Ashok Chatterjee

Abstract The effective hopping of the polaron has been studied for different hole concentrations. Holstein-Hubbard model is used for the half-filled and less than half-filled cases. A series of canonical transformations are imposed on the generic Hamiltonian and considering the strongly interacting electrons, the transformed Hamiltonian has been reconstructed to an effective t-J model. Using the mean-filled Hartree-Fock approximation the electronic Hamiltonian has been solved with the Zuberev’s Green function technique. The effective polaronic transport is found to be strongly dependent on the electron and hole concentration of the system.

IOP Conference Series Materials Science and Engineering•Mar 1, 2022•0 citations

Configuration-interaction approach to hole pairing in the two-dimensional Hubbard model

Enrique Louis, F. Guinea, María P. López-Sancho +1 more

The interactions between holes in the Hubbard model, in the low density, intermediate- to strong-coupling limit, are investigated by systematically improving mean field calculations. The configuration-interaction basis set is constructed by applying to local unrestricted Hartree-Fock configurations all lattice translations and rotations. It is shown that this technique reproduces, correctly, the properties of the Heisenberg model, in the limit of large U. Upon doping, dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. The numerical results also show that when more than two holes are added to the system, they do not tend to cluster, but rather hole pairs remain far apart. Hole-hole correlations are also calculated and shown to be in qualitative agreement with exact calculations for $4\ifmmode\times\else\texttimes\fi{}4$ clusters. In particular our results indicate that for intermediate coupling the hole-hole correlation attains a maximum when the holes are in the same sublattice at a distance of $\sqrt{2}$ times the lattice spacing, in agreement with exact results and the $t\ensuremath{-}J$ model. The method is also used to derive known properties of the quasiparticle band structure of isolated spin polarons.

arXiv:cond-mat/9811298•Physical review. B, Condensed matter•Jun 1, 1999•21 citations

The self-trapping transition in the non-half-filled strongly correlated extended Holstein-Hubbard model in two-dimensions

I. V. Sankar, Ashok Chatterjee

The two-dimensional extended Holstein-Hubbard model (EHH) has been considered at strong correlation regime in the non-half-filled band case to understand the self-trapping transition of electrons in strongly correlated electron system. We have used the method of optimized canonical transformations to transform an EHH model into an effective extended Hubbard (EEH) model. In the strong on-site correlation limit an EH model can be transformed into a t-J model which is finally solved using Hartree-Fock approximation (HFA). We found that, for non-half-filled band case, the transition is abrupt in the adiabatic region whereas it is continuous in the anti-adiabatic region.

AIP conference proceedings•Jan 1, 2014•0 citations

Polarons and bipolarons in strongly interacting electron-phonon systems

Gerhard Wellein, Heinrich Röder, Holger Fehske

The Holstein Hubbard and Holstein t-J models are studied for a wide range of phonon frequencies, electron-electron, and electron-phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron-phonon coupling, in particular in the adiabatic regime. Using parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.

arXiv:cond-mat/9512143•Physical review. B, Condensed matter•Apr 15, 1996•163 citations

Hole pairs in the two-dimensional Hubbard model

Enrique Louis, F. Guinea, María P. López-Sancho +1 more

The interactions between holes in the Hubbard model, in the low-density, inter mediate-to-strong coupling limit, are investigated. Dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. Our results are derived by systematically improving mean-field calculations. The method can also be used to derive known properties of isolated spin polarons.

arXiv:cond-mat/9801157•Europhysics Letters (EPL)•Oct 15, 1998•9 citations

Effect of long-range hopping on Tc in a two-dimensional Hubbard-Holstein model of the cuprates

Ehsan Khatami, Alexandru Macridin, Mark Jarrell

We study the effect of long-range hoppings on ${T}_{c}$ for the two-dimensional (2D) Hubbard model with and without Holstein phonons using parameters evaluated from band-structure calculations for cuprates. Employing the dynamical cluster approximation (DCA) with a quantum Monte Carlo (QMC) cluster solver for a 4-site cluster, we observe that without phonons, the long-range hoppings, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, generally suppress ${T}_{c}$. We argue that this trend remains valid for larger clusters. In the presence of the Holstein phonons, a finite ${t}^{\ensuremath{'}}$ enhances ${T}_{c}$ in the under-doped region for the hole-doped system, consistent with local-density approximation (LDA) calculations and experiment. This is interpreted through the suppression of antiferromagnetic (AF) correlations and the interplay between polaronic effects and the antiferromagnetism.

arXiv:0806.3996•Physical Review B•Aug 8, 2008•22 citations
The Holstein-Hubbard model is studied in two dimensions to explore the nature of polarons as a function of hole concentration in the strong correlation regime. A series of canonical transformations is performed to obtain an effective extended Hubbard model which, in the strong on-site electron-electron correlation regime, transforms into a t-J model and is solved using the mean-field Hartree-Fock approximation (HFA). It is shown that the hopping parameter which is related to the bandwidth of the polaron is very small for low (x ≈ 0) and high (x ≈ 1) hole concentrations whereas the hopping parameter is much larger for the intermediate hole concentrations.
Abstract The effective hopping of the polaron has been studied for different hole concentrations. Holstein-Hubbard model is used for the half-filled and less than half-filled cases. A series of canonical transformations are imposed on the generic Hamiltonian and considering the strongly interacting electrons, the transformed Hamiltonian has been reconstructed to an effective t-J model. Using the mean-filled Hartree-Fock approximation the electronic Hamiltonian has been solved with the Zuberev’s Green function technique. The effective polaronic transport is found to be strongly dependent on the electron and hole concentration of the system.
The interactions between holes in the Hubbard model, in the low density, intermediate- to strong-coupling limit, are investigated by systematically improving mean field calculations. The configuration-interaction basis set is constructed by applying to local unrestricted Hartree-Fock configurations all lattice translations and rotations. It is shown that this technique reproduces, correctly, the properties of the Heisenberg model, in the limit of large U. Upon doping, dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. The numerical results also show that when more than two holes are added to the system, they do not tend to cluster, but rather hole pairs remain far apart. Hole-hole correlations are also calculated and shown to be in qualitative agreement with exact calculations for $4\ifmmode\times\else\texttimes\fi{}4$ clusters. In particular our results indicate that for intermediate coupling the hole-hole correlation attains a maximum when the holes are in the same sublattice at a distance of 2\sqrt{2}2​ times the lattice spacing, in agreement with exact results and the $t\ensuremath{-}J$ model. The method is also used to derive known properties of the quasiparticle band structure of isolated spin polarons.
The two-dimensional extended Holstein-Hubbard model (EHH) has been considered at strong correlation regime in the non-half-filled band case to understand the self-trapping transition of electrons in strongly correlated electron system. We have used the method of optimized canonical transformations to transform an EHH model into an effective extended Hubbard (EEH) model. In the strong on-site correlation limit an EH model can be transformed into a t-J model which is finally solved using Hartree-Fock approximation (HFA). We found that, for non-half-filled band case, the transition is abrupt in the adiabatic region whereas it is continuous in the anti-adiabatic region.
The Holstein Hubbard and Holstein t-J models are studied for a wide range of phonon frequencies, electron-electron, and electron-phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron-phonon coupling, in particular in the adiabatic regime. Using parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.
The interactions between holes in the Hubbard model, in the low-density, inter mediate-to-strong coupling limit, are investigated. Dressed spin polarons in neighboring sites have an increased kinetic energy and an enhanced hopping rate. Both effects are of the order of the hopping integral and lead to an effective attraction at intermediate couplings. Our results are derived by systematically improving mean-field calculations. The method can also be used to derive known properties of isolated spin polarons.
We study the effect of long-range hoppings on Tc{T}_{c}Tc​ for the two-dimensional (2D) Hubbard model with and without Holstein phonons using parameters evaluated from band-structure calculations for cuprates. Employing the dynamical cluster approximation (DCA) with a quantum Monte Carlo (QMC) cluster solver for a 4-site cluster, we observe that without phonons, the long-range hoppings, ${t}^{\ensuremath{'}}$ and ${t}^{\ensuremath{''}}$, generally suppress Tc{T}_{c}Tc​. We argue that this trend remains valid for larger clusters. In the presence of the Holstein phonons, a finite ${t}^{\ensuremath{'}}$ enhances Tc{T}_{c}Tc​ in the under-doped region for the hole-doped system, consistent with local-density approximation (LDA) calculations and experiment. This is interpreted through the suppression of antiferromagnetic (AF) correlations and the interplay between polaronic effects and the antiferromagnetism.