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arXiv:0910.5618 · Physical Review B

Phonon renormalization from local and transitive electron-lattice couplings in strongly correlated systems

Ernst von Oelsen, Andrea Di Ciolo, J. Lorenzana, G. Seibold, M. Grilli

Published Apr 21, 2010• 15 citations
arXivHTMLPDF

Abstract

Within the time-dependent Gutzwiller approximation applied to one-dimensional Holstein and Su-Schrieffer-Heeger-Hubbard models, we study the influence of electron correlations on the phonon self-energy. For the local Holstein coupling, we find that the phonon-frequency renormalization gets weakened upon increasing the on-site interaction $U$ for all momenta. In contrast, correlations can enhance the phonon-frequency shift for small wave vectors in the Su-Schrieffer-Heeger-Hubbard model. Moreover, the time-dependent Gutzwiller approximation applied to the latter model provides a mechanism which leads to phonon-frequency corrections at intermediate momenta due to the coupling with double-occupancy fluctuations. Both models display a shift of the nesting induced to a $q=0$ instability when the on-site interaction becomes sufficiently strong and thus establishing phase separation as a generic phenomenon of strongly correlated electron-phonon coupled systems.

DOI
10.1103/physrevb.81.155116

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Within the time-dependent Gutzwiller approximation applied to one-dimensional Holstein and Su-Schrieffer-Heeger-Hubbard models, we study the influence of electron correlations on the phonon self-energy. For the local Holstein coupling, we find that the phonon-frequency renormalization gets weakened upon increasing the on-site interaction UUU for all momenta. In contrast, correlations can enhance the phonon-frequency shift for small wave vectors in the Su-Schrieffer-Heeger-Hubbard model. Moreover, the time-dependent Gutzwiller approximation applied to the latter model provides a mechanism which leads to phonon-frequency corrections at intermediate momenta due to the coupling with double-occupancy fluctuations. Both models display a shift of the nesting induced to a q=0q=0q=0 instability when the on-site interaction becomes sufficiently strong and thus establishing phase separation as a generic phenomenon of strongly correlated electron-phonon coupled systems.
Studies of Hamiltonians modeling electron-electron (e-e) and electron-phonon (e-ph) coupling have been fundamental in capturing the novel ordering seen in many quasi-one-dimensional condensed matter systems. Extending such studies to quasi-two-dimensional (2D) systems is of great current interest, as e-ph couplings are predicted to play a major role in the stabilization or enhancement of novel phases in 2D material systems. In this work, we study model systems that describe the interplay between the Hubbard coupling and the phonon modes in the Holstein and Su-Schrieffer-Heeger (SSH) Hamiltonians using the functional renormalization group. For both types of e-ph couplings, we find the predicted charge density wave phases in competition with antiferromagnetic ordering. As the system is doped, the transition shifts, with both orders showing incommensurate peaks. We compare the evolution of the quasiparticle weight for the Holstein model with that of the SSH model as the systems transition from antiferromagnetic to charge-ordered ground states. Finally, we calculate the self-energy of the phonon and capture the impact of charge ordering on the phonon modes.
We consider the Hubbard-Holstein model in the adiabatic limit to investigate the effects of electron-electron interactions on the electron-phonon coupling. To this aim we compute at any momentum and filling the static charge susceptibility of the Hubbard model within the Gutzwiller approximation, and we find that electron-electron correlations effectively screen the electron coupling to the lattice. This screening is more effective at large momenta, and as a consequence, the charge-density-wave phase due to the usual Peierls instability of the Fermi-surface momenta is replaced by a phase-separation instability when the correlations are sizable.
We present a dynamical mean-field study of nonperturbative electronic mechanisms, which may lead to significant enhancements of the electron-phonon coupling in correlated electron systems. Analyzing the effects of electronic correlations on the lowest-order electron-phonon processes, we show that in the proximity of the Mott metal-to-insulator transition of the doped square lattice Hubbard model, where the isothermal charge response becomes particularly large at small momenta, the coupling of electrons to the lattice is strongly increased. This, in turn, induces significant corrections to both the electronic self-energy and phonon-mediated pairing interaction, indicating the possible onset of a strong interplay between lattice and electronic degrees of freedom even for small values of the bare electron-phonon coupling.
This thesis investigates the interplay between electron-electron and electron-phonon interactions in low-dimensional lattice models, specifically within the Hubbard model incorporating Su-Schrieffer-Heeger (SSH) coupling with phonons. SSH interactions, which modulate the electron hopping amplitude through lattice displacements, have recently attracted renewed interest due to their potential relevance in strongly correlated materials. The main objective of this work is to determine whether the inclusion of SSH couplings in the Hubbard model can stabilize superconducting or spin-gapped metallic states, as well as other exotic phases of matter. While the half-filled SSH-Hubbard model has been extensively studied in one dimension and only partially examined in two dimensions, its phase diagram in the doped regime remains largely unexplored. This thesis aims to fill this gap, focusing on the emergence of correlated phases away from half-filling in both one and two spatial dimensions. We use the variational Monte Carlo method with a trial wave function defined in a hybrid electron-phonon Hilbert space. In addition to Jastrow factors that account for correlation effects, the wave function includes an antisymmetric component that captures backflow-inspired electron-phonon correlations. This approach enables us to accurately model both electron-electron and electron-phonon interactions. Moreover, since the variational method avoids the sign problem, we can simulate the system in the doped regime, an area typically inaccessible to exact quantum Monte Carlo methods (QMC), which are limited to half-filling. In one dimension, we observe the stabilization of a Luther-Emery liquid, a metallic phase with gapless charge excitations and a finite spin gap, upon doping a Peierls insulating phase. This finding resolves a long-standing debate regarding its realization in SSH chains. Benchmarking with density-matrix renormalization group results confirms the reliability of our approach. In two dimensions, we investigate the SSH-Hubbard model on the square lattice, obtaining results that are consistent with previous exact QMC studies at half-filling. Upon doping, we observe that SSH phonons can induce s-wave superconductivity in the weakly correlated regime. However, we suggest that the enhancement of d-wave superconductivity by SSH coupling in the strongly correlated regime may significantly depend on the specific implementation of the SSH interaction. In one particular case, we find that d-wave superconductivity is slightly suppressed by SSH coupling. These results are further confirmed by a Hartree-Fock analysis performed in the anti-adiabatic limit. Overall, this thesis highlights the crucial role of lattice effects in correlated electron systems, shedding light on the distinct contributions of SSH-type couplings in one and two dimensions. Our findings provide new insights into the microscopic mechanisms behind exotic metallic phases and set the stage for further studies of phonon-mediated phenomena in correlated systems.
Ultrafast pump-probe spectroscopy provides a powerful means to investigate electron-phonon (e-ph) interactions in strongly correlated systems. Nevertheless, the question of how different microscopic e-ph coupling mechanisms influence the lattice's nonequilibrium response has not been widely addressed. We perform time-dependent density matrix renormalization group simulations on a pumped one-dimensional Mott insulator coupled to phonons through either Holstein or Su-Schrieffer-Heeger (SSH) interactions. The electronic responses of the two models are qualitatively similar in the Mott-insulating regime and are governed by the same excitations and resonance conditions of the Hubbard model. In contrast, the lattice dynamics of the two models differ substantially. While the Hubbard-Holstein model exhibits long-lived coherent phonon oscillations when the pump resonates with the bare phonon frequency, no such oscillations are observed for the Hubbard-SSH model. These contrasting responses remain robust against changes in phonon frequency and pump parameters, suggesting that coherent lattice dynamics can provide a direct nonequilibrium probe of the microscopic form of e-ph coupling.
We investigate the effect of strong electron correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model in the presence of charge fluctuations. Specifically, we analyze the momentum modulation of the electron-phonon vertex induced by the electronic correlations. The role of the on-site Coulomb interaction UUU is investigated in different regions of the Brillouin zone. The results reveal the presence of a strong forward scattering peak at low temperatures and, after an initial decrease with UUU, we find that the electron-phonon vertex starts to increase above an intermediate value of the Coulomb interaction. We show that this behavior is related to an incipient phase separation that takes place at a critical value of UUU for fixed doping. A comparison with other approaches is also discussed.