Ground-state properties of the Holstein model near the adiabatic limit

Abstract

We adapt a variational procedure to calculate ground-state properties of the Holstein model in the adiabatic limit. At strong coupling, this adaption leads to rapid convergence of results. The intermediate coupling regime is further handled with an adaptive algorithm. We also use semiclassically derived results for the adiabatic end point, along with weak coupling perturbation theory. These establish weak and strong coupling ͑or large and small polaron, respectively͒ regimes in two dimensions or higher. As is well known, these are connected smoothly, but the crossover becomes increasingly abrupt as the phonon frequency decreases.

Discontinuous polaron transition in a two-band model

“…The carrier-phonon coupling leads to the formation of a polaron, a coherent quasi-particle (QP) consisting of the charge carrier and the cloud of phonons surrounding it and moving coherently with it. Polarons have been studied extensively especially in the Holstein model, [11][12][13][14][15][16][17][18] the simplest model where local phonons modify the on-site energy of the carrier, but also to generalizations with short-range and long-range couplings of similar origin, such as the breathing-mode (BM) model [19][20][21] , the double-well potential model 22,23 and the Fröhlich model 24,25 .…”

“…arXiv:1611.04543v1 [cond-mat.str-el] 14 Nov 2016 which favors k = 0. While some of this physics is similar to that explaining the transition in the SSH model, we find strong indications that the two-band nature of our model plays a vital role.…”

The Effect of Next-Nearest Neighbour Hopping in the One, Two, and Three Dimensional Holstein Model

“…The single polaron problem is solved here with the variational exact diagonalization method described in Bonča et al . 5 and revised by the authors as described in refs 6 , 12 to account for a rapidly growing Hilbert space from the additional terms in the Hamiltonian. For the data included in these plots 20–100 preliminary diagonalizations were performed with the most strongly contributing basis states selected at each iteration to seed the next iteration.…”

“… 5 , and now that problem is effectively solved. Several extensions were subsequently reported, including ones to better manage disparate electron ( t ) and phonon ( ω E ) energy scales (in particular, ω E ≪ t ) 6 7 , higher dimensionality 8 9 10 , extended interaction range 11 12 and inclusion of next-nearest neighbour (NNN) single-particle hopping amplitude 13 . In this last study it was found that including NNN hopping in the one dimensional Holstein model altered significantly the electron’s effective mass in strong coupling.…”

Delocalized Davydov D1 Ansatz for the Holstein polaron

“…A simple Hamiltonian by the name of the Holstein molecular crystal model 14,15 has been extensively used to study polaron properties of molecular and biological systems. Based on the Holstein Hamiltonian, various numerical methods have been proposed to study static and dynamic properties of the Holstein polaron, such as the ground-state energy, the effective polaron mass and radius, [16][17][18][19][20][21] adiabatic behavior, 22 low-energy excitations, 19,23 and the phase diagram. 24 As an exact solution to the Holstein Hamiltonian remains elusive, the weak-coupling perturbation theory (WCPT) 25 and the strong-coupling perturbation theory (SCPT) 26 were used to deal with the weak and strong exciton-phonon coupling regimes, respectively.…”