Spectral properties of the 2D Holstein polaron

Abstract

The two-dimensional Holstein model is studied by means of direct Lanczos diagonalization preserving the full dynamics and quantum nature of phonons. We present numerical exact results for the single-particle spectral function, the polaronic quasiparticle weight, and the optical conductivity. The polaron band dispersion is derived both from exact diagonalization of small lattices and analytic calculation of the polaron self-energy.

Numerical study of theE⊗eJahn-Teller polaron and bipolaron

“…The precision of our results in the thermodynamic limit can be tested in the weak coupling limit, where the optical conductivity threshold is known to be at ω = ω 0 . In this case, other methods, defined on finite systems, show pronounced finite-size effects due to discreteness in the k − space which are reflected in the threshold, larger than ω 0 in the weakcoupling limit [19][20][21], and rather well separated peaks corresponding to scattering of the initial k = 0 electron state into finite-k states. The main signatures of σ reg (ω) at g = 1.0 of both models (JT and HM) are: the spectra are strongly asymmetric in frequency, which is a characteristic of large polarons [24].…”

“…The most efficient methods provide energies for the Holstein polaron problem that are accurate up to 21 digits in the thermodynamic limit [14]. In addition to static quantities, dynamic properties such as spectral functions and optical conductivity of the Holstein model have recently been studied on small lattice clusters [19][20][21][22][23]. However, except in the small polaron regime, such calculations are subject to pronounced finite-size effects.…”

Optical absorption and single-particle excitations in the two-dimensional Holsteint−Jmodel

“…The transition to the lattice hole-polaron state is accompanied by a strong increase in the on-site hole-phonon correlations [27], indicating that the lattice polaron QP comprising a "quasilocalized" hole and the phonon cloud is mainly confined to a single lattice site (small-size lattice hole polaron). Compared to the non-interacting single-electron (Holstein model) [50] or spinless fermion (Holstein-t model) [26] problems, the critical EP coupling strength for lattice polaron formation is considerably reduced due to magnetic prelocalization effects.…”

“…Hence the question arises whether the lattice hole polaron is a "good" QP in the sense that one can construct a QP operator,c Kσ →d Kσ , having large spectral weight at the lowest pole in the spectrum. Indeed, it was demonstrated in recent ED work that it is possible to construct such a composite electron/hole-phonon (polaron) operator by an appropriate phonon dressing ofc Kσ for the Holstein model [50] as well as for the t-J model coupled to buckling/breathing modes [29].…”

“…[35]) and Holstein models [59,60,50] on finite lattices employing ED techniques. First results, obtained recently for the 1D HtJM [32], indicate that EP coupling effects may be at least partly responsible for the experimentally observed frequency dependence of the optical conductivity in the CuO 3 chains of the 1:2:3 family of high-T c oxides.…”