To discuss the interplay of electronic and lattice degrees of freedom in systems with strong Coulomb correlations we have performed an extensive numerical study of the two-dimensional Holstein t-J model. The model describes the interaction of holes, doped in a quantum antiferromagnet, with a dispersionsless optical phonon mode. We apply finite-lattice Lanczos diagonalization, combined with a well-controlled phonon Hilbert space truncation, to the Hamiltonian. The focus is on the dynamical properties. In particular we have evaluated the single-particle spectral function and the optical con-
We calculate de Gennes' extrapolation length for a d-wave superconductor near a surface within Fermiliquid theory. The extrapolation length depends critically on the orientation of the surface relative to the crystal axes and on the surface roughness. This sensitivity of the boundary conditions for a d-wave order parameter to surface conditions is not found in traditional s-wave superconductors, and is a signature of anisotropic pairing with a changing sign of the order parameter along the Fermi surface. de Gennes' method is used to calculate the reduction of T c in thin strips of high-T c superconductors.
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 singlehole 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 inter-site bipolaronic states. At quarter-filling, a polaronic superlattice is formed in the adiabatic strong-coupling regime.Polaronic features of dopant-induced charge carriers have been detected in the copper-based high-T c compounds La 2−x Sr x CuO 4+y , and even more in the isostructural nickel-based chargetransfer oxides La 2−x Sr x NiO 4+y [1]. To tackle the problem of (bi)polaron formation in such systems exhibiting besides a substantial electron-phonon (EP) coupling strong Coulomb interactions, it seems, at the moment, that approximation-free numerical quantum Monte-Carlo and exact diagonalization (ED) analyses of generic model Hamiltonians yield the most reliable results. Along this line, by use of ED, the ground-state properties of Hubbard and t-J models with an on-site Holstein EP coupling have been studied on finite clusters in 1D and 2D [2][3][4]. What is missing to date is an application of the powerful ED technique to the calculation of dynamical properties of the Holstein t-J model (HtJM), including the full quantum nature of phonons.In this contribution, we employ the Lanczos algorithm in combination with a kernel polynomial moment expansion and the Maximum Entropy method [5] to investigate the quasiparticle spectrum of a single hole-polaron in the 2D HtJM on a ten-site square lattice. Moreover, we compute different hole-hole/phonon correlation functions at higher doping level in order to comment on hole-binding effects and charge-densitywave (CDW) formation.The HtJM is described by the Hamiltonian [4]where H ph and H t−J represent the phonon part and standard t-J model, respectively, and the last term takes into account the interaction of doped holes (h i = 1 − σc † iσciσ ) with a single dispersionless phonon mode (which, e.g., may be thought of as representing a local apical-oxygen coupling; ε p -EP coupling constant, ω -bare phonon frequency). H acts in a projected Hilbert space without double occupancy. A general state of (1) can be written as the direct product |Ψ = l,k c k l |l el ⊗ |k ph , where l and k label the electronic and bosonic basic states, respectively, andSince the bosonic part of the Hilbert space is infinite dimensional we use a truncation method [4] restricting ourselves to phononic states with at most M phonons. To control our truncation procedure as a function of M , we calculate the weight of the m-phonon states in the ground state |Ψ 0 of H:In the numerical work convergence is achieved if the relative error of E 0 (M ) is less than 10 −7 . Figure 1 shows |c m | 2 for the 2D HtJM with a single hole at wea...
Employing the Lanczos algorithm in combination with a kernel polynomial moment expansion (KPM) and the maximum entropy method (MEM), we show a way of calculating charge and spin excitations in the Holstein t-J model, including the full quantum nature of phonons. To analyze polaron band formation we evaluate the hole spectral function for a wide range of electron-phonon coupling strengths. For the first time, we present results for the optical conductivity of the 2D Holstein t-J model.Comment: 2 pages, Latex. Submitted to Physica C, Proc. Int. Conf. on M2HTSC
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