Polarons and Bipolarons in Holstein and Holstein t−J models by Dynamical Mean Field Theory

In system with strong electron-phonon (e-ph) interaction, the carriers lose mobility, ultimately acquiring polaronic character. A polaron is a state in which the phonon and electron degrees of freedom are strongly entangled, and the presence of an electron is associated to a finite lattice distortion, which in turn binds the electron leading to the so-called self-trapping effect. Polarons also tend to create bound pairs, called bipolarons of course the presence of Coulomb repulsion destabilize bi-polarons in favor of a pure polaronic state at finite densities [1, 2]. Typical signatures of polarons are seen in multi-peaked photoemission spectra[3] and transport measurements, where an activated behavior with a characteristic energy given by the polaronic binding energy is observed. The polaronic peak found in the mid infrared measurements of optical conductivity [4] may also not only detect the polaronic binding energy [5] but also other subtle polaronic transitions at very low energy [6]. Another less classical indication of polaronic formation comes from the analysis of lattice displacements associated to the excess charge as obtained by the distribution of distances between atoms[3]. A joint analysis of both spectral [5] and local lattice distortions can disentangle various kind of behavior in polaronic systems. In fact we notice that neglecting the repulsive interaction a gapped pair state can be formed even without a significant associated polarization. In this case bipolarons are expected to be a relatively mobile particle. The aim of this work is to provide a thorough analysis of polaronic spectral properties in both single and multi-polaron cases. The backbone of our presentation is the DMFT which is introduced and briefly discussed in general in section 2. In the single polaron case we review the exact solution of the Holstein model [7, 8] (section 4) and we present some new results for the Holstein t − J model comparing our results with those of Mishchenko [9]. At large polaronic densities we use both Exact Diagonalization (ED) and Quantum Monte Carlo (QMC) techniques to solve the DMFT equations for the Holstein model respectively at the T = 0 (sec. 5) and T > 0 (section 6). In this case we compare spinless and spinful fermions cases and we discuss in detail the role of the adiabatic ratio. In this way the properties of a pure polaronic state can be disentangled from those of bipolaronic state. We compare also numerical solutions