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.
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.
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.
Electron-phonon (e-ph) interactions play a crucial role in determining many properties of materials. In this context, the Su-Schrieffer-Heeger (SSH) model, where atomic motion modulates the electronic hopping, has gained significant attention due to its potential for strong electron pairing in relation to high-Tc superconductivity. Previous studies of the SSH models have addressed many aspects of this problem, but have focused heavily on either dilute or half-filled models with dispersionless (Einstein) phonons. Here, we study the effects of dispersive optical phonons on the lightly doped one-dimensional optical Hubbard-SSH model using the density matrix renormalization group. We observe a significant enhancement in singlet binding driven by phonon dispersion; however, by calculating various correlation functions, we find that the enhanced binding does not translate to increased superconducting correlations but rather robust bond correlations in the studied parameter regime. Nevertheless, the significant impact of phonon dispersion on these correlations highlights the need to go beyond the Einstein phonon limit while modeling realistic quantum materials.
The spectral response and physical features of the 2D Hubbard-Holstein model are calculated both in equilibrium at zero and low chemical dopings, and after an ultrashort powerful light pulse, in undoped systems. At equilibrium and at strong charge-lattice couplings, the optical conductivity reveals a three-peak structure in agreement with experimental observations. After an ultrashort pulse and at nonzero electron-phonon interaction, phonon and spin subsystems oscillate with the phonon period T(ph)≈80 fs. The decay time of the phonon oscillations is about 150-200 fs, similar to the relaxation time of the charge system. We propose a criterion for observing these oscillations in high T(c) compounds: the time span of the pump light pulse τ(pump) has to be shorter than the phonon oscillation period T(ph).
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 present a density matrix renormalization group study of the doped one-dimensional (1D) Hubbard-Su-Schrieffer-Heeger (Hubbard-SSH) model, where the atomic displacements linearly modulate the nearest-neighbor hopping integrals. Focusing on an optical variant of the model in the strongly correlated limit relevant for cuprate spin chains, we examine how the SSH interaction modifies the model's ground- and excited-state properties. The SSH coupling weakly renormalizes the model's single- and two-particle response functions for electron-phonon $(e\text{\ensuremath{-}}\mathrm{ph})$ coupling strengths below a parameter-dependent critical value gc. For larger $e\text{\ensuremath{-}}\mathrm{ph}$ coupling, the sign of the effective hopping integrals changes for a subset of orbitals, which drives a lattice dimerization distinct from the standard nesting-driven picture in 1D. The spectral weight of the one- and two-particle dynamical response functions are dramatically rearranged across this transition, with significant changes in the ground-state correlations. We argue that this dimerization results from the breakdown of the linear approximation for the $e\text{\ensuremath{-}}\mathrm{ph}$ coupling and thus signals a fundamental limitation of the linear SSH interaction. Our results have consequences for our understanding of how SSH-like interactions can enter the physics of strongly correlated quantum materials, including the recently synthesized doped cuprate spin chains.
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.