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arXiv:cond-mat/9802181 · Physical review. B, Condensed matter

Optical absorption and single-particle excitations in the two-dimensional Holstein t−J model

B. Bäuml, Gerhard Wellein, Holger Fehske

Published Aug 15, 1998• 76 citations
arXivHTMLPDF

Abstract

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 $t\ensuremath{-}J$ 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 conductivity for characteristic hole-phonon couplings, spin exchange interactions, and phonon frequencies. The results are used to analyze the formation of lattice hole polarons in great detail. Links with experiments on layered perovskites are made. In addition, we compare the Chebyshev recursion and maximum entropy algorithms, used for calculating spectral functions, with standard Lanczos methods.

DOI
10.1103/physrevb.58.3663

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Physical review. B, Condensed matter•Jun 15, 1995•94 citations
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\ensuremath−Jt\ensuremath{-}Jt\ensuremath−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 conductivity for characteristic hole-phonon couplings, spin exchange interactions, and phonon frequencies. The results are used to analyze the formation of lattice hole polarons in great detail. Links with experiments on layered perovskites are made. In addition, we compare the Chebyshev recursion and maximum entropy algorithms, used for calculating spectral functions, with standard Lanczos methods.
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] H = H ph + H t\\GammaJ \\Gamma p " p ¯h! X i \\Gamma b y i + b i \\Delta ~ h i<F25.
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 parallel computers we were able to investigate the transition from ``large'' to ``small'' polarons in detail. By resolving the low-lying eigenstates of the Hamiltonian and by calculating the spectral function, we can identify a polaron band in the strong-coupling case, whose dispersion deviates from the free-particle dispersion at low and intermediate phonon frequencies. For two electrons (holes) we establish the existence of bipolaronic states and discuss the formation of a bipolaron band. For the two-dimensional Holstein t-J model, we demonstrate that the formation of hole polarons is favored by strong Coulomb correlations. Analyzing hole-hole correlation functions, we find that hole binding is enhanced as a dynamical effect of the electron-phonon interaction. \textcopyright{} 1996 The American Physical Society.
We derive an exact solution for the optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ of one hole in the Holstein $t\text{\ensuremath{-}}J$ model in the framework of dynamical mean-field theory. We investigate the magnetic and phonon features associated with polaron formation as a function of the exchange coupling JJJ, electron-phonon interaction $\ensuremath{\lambda}$, and temperature. Our solution directly relates the features of the optical conductivity to excitations in the single-particle spectral function, revealing two distinct mechanisms of closing and filling of the optical pseudogap that take place upon varying the microscopic parameters. We show that the optical absorption at the polaron crossover is characterized by a coexistence of a magnon peak at low frequency and a broad polaronic band at higher frequency. An analytical expression for $\ensuremath{\sigma}(\ensuremath{\omega})$ valid in the polaronic regime is presented.
We study static and dynamic properties of an electron coupled to dispersive quantum optical phonons in the framework of the Holstein model defined on a one-dimensional lattice. Calculations are performed using the Lanczos algorithm based on a highly efficient construction of the variational Hilbert space. Even small phonon dispersion has a profound effect on the low-energy optical response. While the upward phonon dispersion broadens the optical spectra due to single-phonon excitations, the downward dispersion has the opposite effect. With increasing dispersion, a multiphonon excitation (MPE) state becomes the lowest excited state of the system at zero momentum and determines the low-frequency response of the optical conductivity where the threshold for optical absorption moves below the single-phonon frequency. Multiphonon states form a well-defined bandlike feature just above the polaron band as clearly seen in the electron spectral function. Low-energy MPEs should be observable in systems with strong optical phonon dispersion in optical as well as angle-resolved photoemission experiments.
We study the dynamical properties of the two-dimensional square lattice Holstein Hamiltonian using numerically exact determinant quantum Monte Carlo simulations. In particular, we report systematic calculations of the model's single-particle spectral function and optical conductivity over a range of phonon energies, electron-phonon coupling strengths, carrier concentrations, and temperatures. In doing so, we map the evolution of the system from a dressed metallic phase to a (bi)polaron liquid/insulator to a charge-density-wave insulator as the carrier concentration is tuned from dilute values to half-filling. We corroborate these results using several equal-time correlation measurements and related proxy quantities reconstructed from time-displaced correlation measurements. This paper is also accompanied by an extensive open data set, covering over 16,640 unique parameter values.
Polaronic features of dopant-induced charge carriers are manifest in recent experiments on ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Srx{\mathrm{Sr}}_{\mathit{x}}Srx​CuO4+y{\mathrm{CuO}}_{4+\mathit{y}}CuO4+y​ and ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$Nix{\mathrm{Ni}}_{\mathit{x}}Nix​CuO4+y{\mathrm{CuO}}_{4+\mathit{y}}CuO4+y​. To study the formation of hole (bi)polarons in such systems exhibiting strong Coulomb interactions, the Holstein t-J model is examined by means of a variational diagonalization technqiue for a wide range of phonon frequencies and electron-phonon (EP) couplings on finite square lattices, up to 18 effective sites in size. Including static displacement field, polaron, and squeezing effects, our approach allows for the description of nearly free polarons in the weak-coupling limit as well as for adiabatic Holstein polarons and nonadiabatic Lang-Firsov polarons in the case of strong EP interactions. At low doping levels and low phonon frequencies we demonstrate that antiferromagnetic spin correlations and EP interactions reinforce each other to the effect of lowering the threshold for polaronic self-localization in a strongly distorted lattice. This is contrasted with the nonadiabatic regime, where we observe the formation of Lang-Firsov polarons with moderate polaronic mass enhancement in a nearly undistorted lattice. In the case of two doped holes, the hole binding energy is analyzed in detail and we find that hole binding is enhanced as a dynamical (static) effect of a rather weak (extremely strong) EP interaction for delocalized (self-trapped) polarons. At quarter-filling we notice, in the adiabatic regime, a sequence of transitions as the EP coupling increases from nearly free mobile polarons to a polaronic superlattice and finally to a charge-separated state. The ordering of polarons disappears at higher phonon frequencies.