We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.We present a numerical study of the Hubbard-Holstein model in one dimension at half filling, including finite-frequency quantum phonons. At half filling, the effects of the electron-phonon and electron-electron interactions compete with the Holstein phonon coupling acting as an effective negative Hubbard on-site interaction U that promotes on-site electron pairs and a Peierls charge-density wave state. Most previous work on this model has assumed that only Peierls or Mott phases are possible at half filling. However, there has been speculation that a third metallic phase exists between the Peierls and Mott phases. We confirm the intermediate phase, and show that the Luttinger liquid correlation exponent K(rho) >1 in this region, indicating dominant superconducting pair correlations. We explore the full phase diagram as a function of Hubbard U, phonon coupling constant, and phonon frequency.

arXiv:cond-mat/0505184Physical Review LettersAug 26, 200594 citations

Phase diagram of the one-dimensional Hubbard-Holstein model at quarter filling

Sahinur Reja, Sudhakar Yarlagadda, P. B. Littlewood

We derive an effective Hamiltonian for the one-dimensional Hubbard-Holstein model, valid in a regime of both strong electron-electron (e-e) and electron-phonon (e-ph) interactions and in the nonadiabatic limit ($t/{\ensuremath{\omega}}_{0}\ensuremath{\le}1$), by using a nonperturbative approach. We obtain the phase diagram at quarter filling by employing a modified Lanczos method and studying various density-density correlations. The spin-spin AF (antiferromagnetic) interactions and nearest-neighbor repulsion, resulting from the e-e and the e-ph interactions, respectively, are the dominant terms (compared to hopping) and compete to determine the various correlated phases. As e-e interaction $(U/t)$ is increased, the system transits from an AF cluster to a correlated singlet phase through a discontinuous transition at all strong e-ph couplings $2\ensuremath{\le}g\ensuremath{\le}3$ considered. At higher values of $U/t$ and moderately strong e-ph interactions ($2\ensuremath{\le}g\ensuremath{\le}2.6$), the singlets break up to form an AF order and then to a paramagnetic order all in a single sublattice; whereas at larger values of $g$ ( $>$ $2.6$ ), the system jumps directly to the spin disordered charge-density-wave (CDW) phase.We derive an effective Hamiltonian for the one-dimensional Hubbard-Holstein model, valid in a regime of both strong electron-electron (e-e) and electron-phonon (e-ph) interactions and in the nonadiabatic limit ($t/{\ensuremath{\omega}}_{0}\ensuremath{\le}1$), by using a nonperturbative approach. We obtain the phase diagram at quarter filling by employing a modified Lanczos method and studying various density-density correlations. The spin-spin AF (antiferromagnetic) interactions and nearest-neighbor repulsion, resulting from the e-e and the e-ph interactions, respectively, are the dominant terms (compared to hopping) and compete to determine the various correlated phases. As e-e interaction $(U/t)$ is increased, the system transits from an AF cluster to a correlated singlet phase through a discontinuous transition at all strong e-ph couplings $2\ensuremath{\le}g\ensuremath{\le}3$ considered. At higher values of $U/t$ and moderately strong e-ph interactions ($2\ensuremath{\le}g\ensuremath{\le}2.6$), the singlets break up to form an AF order and then to a paramagnetic order all in a single sublattice; whereas at larger values of $g$ ($>$$2.6$), the system jumps directly to the spin disordered charge-density-wave (CDW) phase.

arXiv:1012.2542Physical Review BAug 25, 201122 citations

Ground-state phase diagram of the 1-D Holstein–Hubbard model

Mohammed Zahid Malik, Soma Mukhopadhyay, Ashok Chatterjee

Physics Letters AFeb 5, 20198 citations

(U/t)

is increased, the system transits from an AF cluster to a correlated singlet phase through a discontinuous transition at all strong e-ph couplings $2\ensuremath{\le}g\ensuremath{\le}3$ considered. At higher values of

U/t

and moderately strong e-ph interactions ($2\ensuremath{\le}g\ensuremath{\le}2.6$), the singlets break up to form an AF order and then to a paramagnetic order all in a single sublattice; whereas at larger values of

g

(

>

2.6

), the system jumps directly to the spin disordered charge-density-wave (CDW) phase.