Competition Between Antiferromagnetic and Charge-Density-Wave Order in the Half-Filled Hubbard-Holstein Model

Abstract

We present a determinant quantum Monte Carlo study of the competition between instantaneous on-site Coulomb repulsion and retarded phonon-mediated attraction between electrons, as described by the two dimensional Hubbard-Holstein model. At half filling, we find a strong competition between antiferromagnetism (AFM) and charge density wave (CDW) order. We demonstrate that a simple picture of AFM-CDW competition that incorporates the phonon mediated attraction into an effective-U Hubbard model requires significant refinement. Specifically, retardation effects slow the onset of charge order, so that CDW order remains absent even when the effective U is negative. This delay opens a window where neither AFM nor CDW order is well established, and where there are signatures of a possible metallic phase.PACS numbers: 71.10. Fd, 71.30.+h, 71.45.Lr, The electron-phonon (el-ph) interaction is responsible for many phenomena in condensed matter physics, including charge density waves (CDWs) and conventional superconductivity. While the el-ph interaction is well understood in metals, the role of phonons in strongly correlated systems is less clear, in part because the interplay of strong electron-electron (el-el) and el-ph interactions can lead to competing ordered phases. Despite its difficulty, this is an important problem to solve because multiple experimental probes have detected signatures of significant lattice effects in strongly correlated materials. For example, in the cuprate high-temperature superconductors, angle-resolved photoemission spectroscopy (ARPES) has observed "kinks" in the band dispersion, which have been attributed to the el-ph interaction, 1 as well as small polaron formation in undoped Ca 2−x Na x CuOCl 2 . 2,3 Additional evidence for a significant el-ph interaction include strong quasiparticle renormalizations detected by STM, 4 and studies which have qualitatively reproduced optical conductivity peaks by including phonons. 5,6 Besides the cuprates, other materials with both strong el-el and el-ph interactions include the manganites 7 and fullerenes. 8On general grounds, two effects are expected when elph interactions are included in a system with strong el-el repulsion. The first is that the two interactions renormalize each other. The phonons mediate a retarded attractive el-el interaction, thus reducing the effective Coloumb repulsion, while the el-el repulsion suppresses charge fluctuations, and hence the el-ph interaction, which couples to them. The second effect is a reduction in the quasiparticle weight due to additional scattering processes, which at large el-ph couplings can lead to a polaron crossover.A natural model for studying the interplay of the elel and el-ph interactions is the Hubbard-Holstein (HH) model, which has been studied using various numerical approaches producing sometimes contradicting results. Within dynamical mean field theory (DMFT), the suppression of the el-ph interaction depends on the underlying phase, and antiferromagnetic (AFM)-DMFT has found a moderate increase i...

Determinant quantum Monte Carlo study of the two-dimensional single-band Hubbard-Holstein model

“…Here, in the finite T 2D case, we find indications of such a phase. 73 This is most clearly seen in the spectral weight at the Fermi level, which is related to G(τ = β/2) 73 and is shown in Fig. 1b.…”

“…[69][70][71][72] Recently this work was extended and a finite temperature phase diagram was proposed for the twodimensional (2D) case at half-filling using determinant quantum Monte Carlo (DQMC). 73 Fig. 1 sketches the result, extending the diagram shown in Fig.…”

“…The point of maximal spectral weight lays near the line where n ↑ n ↓ = 0.25, a value equal to that expected for a paramagnetic metal. Furthermore, as the temperature is lowered, the low energy spectral weight in the intervening phase grows, indicative of metallic behavior, while the spectral weight in the large U and λ regimes falls, as expected for an insulator 73 . These results are in contrast to the results obtained in infinite dimensions and T = 0 where a first order AFM/CDW transition has been proposed.…”

“…However, for small Ω, retardation effects can become important as observed in comparisons between the HH and U eff Hubbard models when one examines observables such as the CDW and AFM susceptibilities. 61,73 Nevertheless, the frequencyindependent U eff model is used often to describe the HH model and recent studies have found that some of the low-energy properties of the model can be captured by such an approximation. 61,69 B.…”

“…When both interactions are present the tendency towards these incompatible orders clearly will compete. [69][70][71][72][73] Competing orders in correlated systems is a prominent issue and a common theme in many transition metal oxides where novel physics often emerges at the boundary between orders.…”