Excitation Spectrum of the Holstein Model

We propose a new density matrix renormalization group (DMRG) approach to study lattices including bosons. The key to the new approach is an exact mapping of a boson site containing 2^N states to N pseudo-sites, each with 2 states. The pseudo-sites can be viewed as the binary digits of a boson level. We apply the pseudo-site DMRG method to the polaron problem in the one- and two-dimensional Holstein models. Ground state results are presented for a wide range of electron-phonon...

We present numerically exact solutions to the problem of a single electron interacting through a long range interaction with optical phonons in two and three dimensions. Comparisons are made with results for the standard Holstein model, and with perturbative approaches from both the weak coupling and strong coupling sides. We find, in agreement with earlier work, that the polaron effective mass increases (decreases) in the weak (strong) coupling regime, respectively. However,...

We describe the formation and properties of Holstein polarons in the entire parameter regime. Our presentation focuses on the polaron mass and radius, which we obtain with an improved numerical technique. It is based on the combination of variational exact diagonalization with an improved construction of phonon states, providing results even for the strong coupling adiabatic regime. In particular we can describe the formation of large and heavy adiabatic polarons. A compariso...

We calculate the spectral properties of the one-dimensional Holstein and breathing polarons using the self-consistent Born approximation. The Holstein model electron-phonon coupling is momentum independent while the breathing coupling increases monotonically with the phonon momentum. We find that for a linear or tight binding electron dispersion: i) for the same value of the dimensionless coupling the quasiparticle renormalization at small momentum in the breathing polaron is...

Using the momentum average approximation we study the importance of adding higher-than-linear terms in the electron-phonon coupling on the properties of single polarons described by a generalized Holstein model. For medium and strong linear coupling, even small quadratic electron-phonon coupling terms are found to lead to very significant quantitative changes in the properties of the polaron, which cannot be captured by a linear Holstein Hamiltonian with renormalized paramete...

It is generally accepted that the dynamical mean field theory gives a good solution of the Holstein model, but only in dimensions greater than two. Here, we show that this theory, which becomes exact in the weak coupling and in the atomic limit, provides an excellent, numerically cheap, approximate solution for the spectral function of the Holstein model in the whole range of parameters, even in one dimension. To establish this, we make a detailed comparison with the spectral...

Ground-state and dynamical properties of the 2D Holstein t-J model are examined by means of direct Lanczos diagonalization, using a truncation method of the phononic Hilbert space. The single-hole spectral function shows the formation of a narrow hole-polaron band as the electron-phonon coupling increases, where the polaronic band collapse is favoured by strong Coulomb correlations. In the two-hole sector, the hole-hole correlations unambiguously indicate the existence of int...

We derive an effective polaronic interaction Hamiltonian, {\it exact to second order in perturbation}, for the spinless one-dimensional Holstein model. The small parameter is given by the ratio of the hopping term ($t$) to the polaronic energy ($g^2 \omega_0$) in all the region of validity for our perturbation; however, the exception being the regime of extreme anti-adiabaticity ($t/\omega_0 \le 0.1$) and small electron-phonon coupling ($g < 1$) where the small parameter is $...

The paper deals with the ground and the first excited state of the polaron in the one dimensional Holstein model. Various variational methods are used to investigate both the weak coupling and strong coupling case, as well as the crossover regime between them. Two of the methods, which are presented here for the first time, introduce interesting elements to the understanding of the nature of the polaron. Reliable numerical evidence is found that, in the strong coupling regime...

The Holstein Hubbard and Holstein t--J models are studied for a wide range of phonon frequencies, electron--electron and electron--phonon interaction strengths on finite lattices with up to ten sites by means of direct Lanczos diagonalization. Previously the necessary truncation of the phononic Hilbert space caused serious limitations to either very small systems (four or even two sites) or to weak electron--phonon coupling, in particular in the adiabatic regime. Using parall...