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Journal of the Physical Society of Japan

Hole Propagation in a 2D Quantum Spin-1/2 Antiferromagnet. II. Effect of FiniteJCorrection

Yoshinori Takahashi, Hirokazu Tsunetsugu

Published Aug 15, 1990• 1 citation
Publisher

Abstract

Single hole propagation doped into a quantum antiferromagnet is studied taking into account the effect of finite exchange interaction up to the first order among antiferromagnetic spin background. Both even and odd moments of the hole density of states are evaluated. The results of the lower order moments suggest the existence of the string effect, which favors the hole localization in the small concentration region.

DOI
10.1143/jpsj.59.2931

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arXiv:cond-mat/0511459•Physical Review B•Jun 21, 2005•1 citation
Single hole propagation doped into a quantum antiferromagnet is studied taking into account the effect of finite exchange interaction up to the first order among antiferromagnetic spin background. Both even and odd moments of the hole density of states are evaluated. The results of the lower order moments suggest the existence of the string effect, which favors the hole localization in the small concentration region.
Within the Schwinger-boson approach for the t-J model, the single hole problem in a two-dimensional quantum antiferromagnet is studied by using the quantum Bogoliubovde Gennes formalism which treats the distortion of the spin background and quantum spin fluctuations on an equal footing. Several self-trapped localized hole states are found in the distorted spin-background as in the case of an anisotropic Heisenberg model. These localized hole states survive at finite temperatures when the antiferromagnetic order becomes short-ranged. The energy separation between the two lowest states is reduced by considering the spin-background distortion, but it remains finite.
The spectral function of a single hole moving in a two-dimensional antiferromagnetic background is calculated, using the self-consistent Born approximation for the self-energy. For small systems, good agreement is found with the results of exact diagonalization studies. In the thermodynamic limit, the quasiparticle residue, the effective mass, and the incoherent multiple spin-wave background are determined as functions of the ratio of Heisenberg exchange J and hopping amplitude t. The relevance of the single-hole results to the physical problem of a finite hole concentration is briefly discussed.
Based on the $t\ensuremath{-}J$ model, it is shown that a hole moving on an antiferromagnetic spin background always induces a phase-string effect. Such a previously unnoticed phase string is revealed by explicitly tracking the Marshall sign and can be rigorously shown to be nonrepairable at low energy. Its quantum interference can drastically modify the long-wavelength behavior of the doped hole, leading to a vanishing spectral weight ZZZ at the ground-state energy. Implication for finite doping is also discussed.
Layered structures of the high Tc superconductors have reinstigated the study of two dimensional (2D) antiferromagnetic spin systems and their charge dynamics for more than a couple of decades now. As a hole moves through such a system it interacts with spin waves and phonons at finite temperature. This book contains systematic derivation of the hole spectral functions in a 2D t-J model and its extensions numerically by first finding the spin waves using linear spin wave approximation and then solving the hole Dyson's equation within the Non-crossing approximation. The role of different parameters and scenario on the hole dynamics in such a system is investigated in detail. Particularly the three main chapters in this book deals with hole dynamics (i) when optical phonons are present in the system at finite temperature, (ii) when small but finite hole density is present in the system and (iii) when periodic antiferromagnetic domain walls are present. This book shows computational results extrapolated to thermodynamic limit and its comparison with the angle-resolved-photo-emission spectra of the high Tc Cuprates in order to understand some aspects of charge flow in such compounds.
We calculate the spin correlation function and the magnetic longitudinal and transverse susceptibilities of a two-dimensional antiferromagnet doped with a small concentration of holes, in the $t\text{\ensuremath{-}}J$ model. We find that the motion of holes generates spin fluctuations that add to the quantum fluctuations, the spin correlations decaying with the inverse of the spin distance, while increasing with doping as the critical hole concentration, where the long-range order disappears, is approached. Moreover, the longitudinal susceptibility becomes finite in the presence of doping due to the strong damping effects induced by the hole motion, while the transverse susceptibility is renormalized by softening effects. Both the longitudinal and transverse susceptibilities increase with doping, the former more significantly than the latter. Our results imply that doping destroys the long-range order while local antiferromagnetic spin correlations persist. This is consistent with experiments on doped copper oxide superconductors.