TY - GEN

T1 - Quantum phase transitions in one-dimensional electron-phonon systems

AU - Fehske, H.

AU - Jeckelmann, E.

PY - 2006

Y1 - 2006

N2 - In this report we have addressed the important problem of quantum phase transitions in one-dimensional strongly coupled electron-phonon systems. As a generic model we analysed the Holstein Hubbard model at half-filling. Applying numerical diagonalisation methods we obtained, by the use of present-day leading-edge supercomputers, basically exact results for both ground-state and spectral properties in the overall region of electron-electron/electron-phonon coupling strengths and phonon frequencies. For the spinless Holstein model we found that for weak EP couplings the system resides in a metallic (gapless) phase described by two non-universal Luttinger-liquid parameters. The renormalised charge velocity and the correlation exponent are obtained by DMRG from finite-size scaling relations, fulfilled with great accuracy. The Luttingerliquid phase splits in an attractive and repulsive regime at low and high phonon frequencies, respectively. Here the polaronic metal, realised for repulsive interactions, is characterised by a strongly reduced mobility of the charge carriers. Increasing the EP interaction, a crossover between Luttinger-liquid and charge-density-wave behaviour is found. The transition to the CDW state is accompanied by significant changes in the optical response of the system. Most notably seems to be the substantial spectral weight transfer from the Drude to the regular part of the optical conductivity, indicating the increasing importance of inelastic scattering processes in the CDW (PI) regime. For the much more involved Holstein Hubbard model, with respect to the metal the electron-electron interaction favours a Mott insulating state whereas the EP coupling is responsible for the Peierls insulator to occur (see fig. 12). True long-range (CDW) order is established in the PI phase only. The PI typifies a band insulator in the adiabatic weak to intermediate coupling range or a bipolaronic insulator for non-to-antiadiabatic strong coupling. Our results for the single-particle spectra indicate that while polaronic features emerge only at strong EP couplings, pronounced phonon signatures, such as multi-phonon bound states inside the CDW gap, can be found in the Mott insulating regime as well. This might be of great importance for interpreting photoemission experiments of lowdimensional materials such as MX-chain compounds. The optical conductivity shows different absorption features in the MI and PI as well and signals that the quantum phase transition between these phases is connected to a change in the ground-state siteparity eigenvalue (of a finite HHM systems with PBC). From our conductivity data we found evidence for only one critical point separating Peierls and Mott insulating phases in the Holstein Hubbard model with dynamical phonons. This differs from the results obtained in the adiabatic limit (ω0 = 0), where two successive transitions have been detected for weak couplings u, λ 〈 1 [26]. The Peierls to Mott transition scenario is corroborated by the behaviour of the spin and charge excitation gaps. From a DMRG finite-size scaling we found δc = δs and δc > δs = 0 in the PI and MI, respectively. The emerging physical picture can be summarised by the phase diagram shown in fig. 12.

AB - In this report we have addressed the important problem of quantum phase transitions in one-dimensional strongly coupled electron-phonon systems. As a generic model we analysed the Holstein Hubbard model at half-filling. Applying numerical diagonalisation methods we obtained, by the use of present-day leading-edge supercomputers, basically exact results for both ground-state and spectral properties in the overall region of electron-electron/electron-phonon coupling strengths and phonon frequencies. For the spinless Holstein model we found that for weak EP couplings the system resides in a metallic (gapless) phase described by two non-universal Luttinger-liquid parameters. The renormalised charge velocity and the correlation exponent are obtained by DMRG from finite-size scaling relations, fulfilled with great accuracy. The Luttingerliquid phase splits in an attractive and repulsive regime at low and high phonon frequencies, respectively. Here the polaronic metal, realised for repulsive interactions, is characterised by a strongly reduced mobility of the charge carriers. Increasing the EP interaction, a crossover between Luttinger-liquid and charge-density-wave behaviour is found. The transition to the CDW state is accompanied by significant changes in the optical response of the system. Most notably seems to be the substantial spectral weight transfer from the Drude to the regular part of the optical conductivity, indicating the increasing importance of inelastic scattering processes in the CDW (PI) regime. For the much more involved Holstein Hubbard model, with respect to the metal the electron-electron interaction favours a Mott insulating state whereas the EP coupling is responsible for the Peierls insulator to occur (see fig. 12). True long-range (CDW) order is established in the PI phase only. The PI typifies a band insulator in the adiabatic weak to intermediate coupling range or a bipolaronic insulator for non-to-antiadiabatic strong coupling. Our results for the single-particle spectra indicate that while polaronic features emerge only at strong EP couplings, pronounced phonon signatures, such as multi-phonon bound states inside the CDW gap, can be found in the Mott insulating regime as well. This might be of great importance for interpreting photoemission experiments of lowdimensional materials such as MX-chain compounds. The optical conductivity shows different absorption features in the MI and PI as well and signals that the quantum phase transition between these phases is connected to a change in the ground-state siteparity eigenvalue (of a finite HHM systems with PBC). From our conductivity data we found evidence for only one critical point separating Peierls and Mott insulating phases in the Holstein Hubbard model with dynamical phonons. This differs from the results obtained in the adiabatic limit (ω0 = 0), where two successive transitions have been detected for weak couplings u, λ 〈 1 [26]. The Peierls to Mott transition scenario is corroborated by the behaviour of the spin and charge excitation gaps. From a DMRG finite-size scaling we found δc = δs and δc > δs = 0 in the PI and MI, respectively. The emerging physical picture can be summarised by the phase diagram shown in fig. 12.

UR - http://www.scopus.com/inward/record.url?scp=62749091820&partnerID=8YFLogxK

U2 - 10.3254/1-58603-609-2-297

DO - 10.3254/1-58603-609-2-297

M3 - Conference contribution

AN - SCOPUS:62749091820

SN - 1586036092

SN - 9781586036096

T3 - Proceedings of the International School of Physics "Enrico Fermi"

SP - 297

EP - 311

BT - Proceedings of the International School of Physics "Enrico Fermi"

T2 - International School of Physics "Enrico Fermi": Polarons in Bulk Materials and Systems with Reduced Dimensionality

Y2 - 21 June 2005 through 1 July 2005

ER -