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Register a new userPhase competition in a one-dimensional three-orbital Hubbard-Holstein model
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We study the interplay between the electron-phonon (e-ph) and on-site electron-electron (e-e) interactions in a three-orbital Hubbard-Holstein model on an extended one-dimensional lattice using determinant quantum Monte Carlo. For weak e-e and e-ph interactions, we observe a competition between an orbital-selective Mott phase (OSMP) and a (multicomponent) charge-density-wave (CDW) insulating phase, with an intermediate metallic phase located between them. For large e-e and e-ph couplings, the OSMP and CDW phases persist, while the metallic phase develops short-range orbital correlations and becomes insulating when both the e-e and e-ph interactions are large but comparable. Many of our conclusions are in line with those drawn from a prior dynamical mean field theory study of the two-orbital Hubbard-Holstein model [Phys. Rev. B 95, 12112(R) (2017)] in infinite dimension, suggesting that the competition between the e-ph and e-e interactions in multiorbital Hubbard-Holstein models leads to rich physics, regardless of the dimension of the system.
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We present electron and phonon spectral functions calculated from determinant quantum Monte Carlo simulations of the half-filled two-dimensional Hubbard-Holstein model on a square lattice. By tuning the relative electron-electron ($e$-$e$) and electron-phonon ($e$-$ph$) interaction strengths, we show the electron spectral function evolving between antiferromagnetic insulating, metallic, and charge density wave insulating phases. The phonon spectra concurrently gain a strong momentum dependence and soften in energy upon approaching the charge density wave phase. In particular, we study how the $e$-$e$ and $e$-$ph$ interactions renormalize the spectra, and analyze how the interplay of these interactions influence the spectral renormalizations. We find that the presence of both interactions suppresses the amount of renormalization at low energy, thus allowing the emergence of a metallic phase. These findings demonstrate the importance of considering the influence of multiple interactions in spectroscopically determining any one interaction strength in strongly correlated materials.
The Hubbard-Holstein model describes fermions on a discrete lattice, with on-site repulsion between fermions and a coupling to phonons that are localized on sites. Generally, at half-filling, increasing the coupling $g$ to the phonons drives the system towards a Peierls charge density wave state whereas increasing the electron-electron interaction $U$ drives the fermions into a Mott antiferromagnet. At low $g$ and $U$, or when doped, the system is metallic. In one-dimension, using quantum Monte Carlo simulations, we study the case where fermions have a long range coupling to phonons, with characteristic range $xi$, interpolating between the Holstein and Frohlich limits. Without electron-electron interaction, the fermions adopt a Peierls state when the coupling to the phonons is strong enough. This state is destabilized by a small coupling range $xi$, and leads to a collapse of the fermions, and, consequently, phase separation. Increasing interaction $U$ will drive any of these three phases (metallic, Peierls, phase separation) into a Mott insulator phase. The phase separation region is once again present in the $U e 0$ case, even for small values of the coupling range.
We study non-local correlations in a three-orbital Hubbard model defined on an extended one-dimensional chain using determinant quantum Monte Carlo and density matrix renormalization group methods. We focus on a parameter with robust Hunds coupling, which produces an orbital selective Mott phase (OSMP) at intermediate values of the Hubbard U, as well as an orbitally ordered ferromagnetic insulating state at stronger coupling. An examination of the orbital and spin-correlation functions indicates that the orbital ordering occurs before the onset of magnetic correlations in this parameter regime as a function of temperature. In the OSMP, we find that the self-energy for the itinerant electrons is momentum dependent, indicating a degree of non-local correlations while the localized electrons have largely momentum independent self-energies. These non-local correlations also produce relative shifts of the hole-like and electron-like bands within our model. The overall momentum dependence of these quantities is strongly suppressed in the orbitally-ordered insulating phase.
We study the interplay between the electron-electron (e-e) and the electron-phonon (e-ph) interactions in the two-orbital Hubbard-Holstein model at half filling using the dynamical mean field theory. We find that the e-ph interaction, even at weak couplings, strongly modifies the phase diagram of this model and introduces an orbital-selective Peierls insulating phase (OSPI) that is analogous to the widely studied orbital-selective Mott phase (OSMP). At small e-e and e-ph coupling, we find a competition between the OSMP and the OSPI, while at large couplings, a competition occurs between Mott and charge-density-wave (CDW) insulating phases. We further demonstrate that the Hunds coupling influences the OSPI transition by lowering the energy associated with the CDW. Our results explicitly show that one must be cautious when neglecting the e-ph interaction in multiorbital systems, where multiple electronic interactions create states that are readily influenced by perturbing interactions.
We study photoinduced ultrafast coherent oscillations originating from orbital degrees of freedom in the one-dimensional two-orbital Hubbard model. By solving the time-dependent Schrodinger equation for the numerically exact many-electron wave function, we obtain time-dependent optical response functions. The calculated spectra show characteristic coherent oscillations that vary with the frequency of probe light. A simple analysis for the dominant oscillating components clarifies that these photoinduced oscillations are caused by the quantum interference between photogenerated states. The oscillation attributed to the Raman-active orbital excitations (orbitons) clearly appears around the charge-transfer peak.
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