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arXiv:cond-mat/0304144 · The European Physical Journal B

Recursion method and one-hole spectral function of the Majumdar-Ghosh model

Roman O. Kuzian, R. Hayn, Johannes Richter

Published Sep 1, 2003• 2 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2003-00252-x

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Using an approximation method for eigenvalue distribution functions, we study the temperature dependence of specific heat of the antiferromagnetic Heisenberg model on the asymmetric railroad-trestle lattice. This model contains both the sawtooth-lattice and Majumdar-Ghosh models as special cases. Making extrapolations to the thermodynamic limit using finite size data up to 28 spins, it is found that specific heat of the Majumdar-Ghosh model has a two-peak structure in its temperature dependence and those of systems near the sawtooth-lattice point have a three-peak structure.

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The spectral function of one hole in different magnetic states of the one-dimensional $t\ensuremath{-}J$ model including three-site term and frustration ${J}^{\ensuremath{'}}$ is studied. In the strong-coupling limit $\stackrel{\ensuremath{\rightarrow}}{J}0$ (corresponding to $\stackrel{\ensuremath{\rightarrow}}{U}\ensuremath{\infty}$ of the Hubbard model) a set of eigenoperators of the Liouvillian is found which allows us to derive an exact expression for the one-particle Green's function that is also applicable at finite temperature and in an arbitrary magnetic state. The spinon dispersion of the pure $t\ensuremath{-}J$ model with the ground state of the Heisenberg model can be obtained by treating the corrections due to a small exchange term by means of the projection method. The spectral function for the special frustration ${J}^{\ensuremath{'}}=J/2$ with the Majumdar-Ghosh wave function is discussed in detail. Besides the projection method, a variational ansatz with the set of eigenoperators of the t term is used. We find a symmetric spinon dispersion around the momentum $k=\ensuremath{\pi}/(2a)$ and a strong damping of the holon branch. Below the continuum a bound state is obtained with finite spectral weight and a very small separation from the continuum. Furthermore, the spectral function of the ideal paramagnetic case at a temperature ${k}_{B}T\ensuremath{\gg}J$ is discussed.
Experimental and numerical spectroscopy have revealed rich physics in antiferromagnets, in particular in frustrated and doped systems. The Majumdar-Ghosh (MG) model has an analytically known spin-disordered ground state of dimerized singlets as a result of magnetic frustration. Here we study the single-hole angle-resolved photoemission spectrum (ARPES) of a doped MG model, where we introduce a spin-hole interaction that is experimentally accessible with ultracold molecules. We report a bound spinon-holon ground state and clear signatures of a spinon-holon molecule state and polarons in the ARPES spectrum at different magnetizations. Moreover, we find signatures of an emergent Feshbach resonance with tunable interactions associated with the unbinding of the spinon and the holon. Our results provide new insights into the physics of dopants in frustrated t − J models and establish the latter as a new platform for studies of emergent few-body phenomena.
Using an approximation method for eigenvalue distribution functions, we study the temperature dependence of specific heat of the antiferromagnetic Heisenberg model on the asymmetric railroad-trestle lattice. This model contains both the sawtooth-lattice and Majumdar-Ghosh models as special cases. Making extrapolations to the thermodynamic limit using finite size data up to 28 spins, it is found that specific heat of the Majumdar-Ghosh model has a two-peak structure in its temperature dependence and those of systems near the sawtooth-lattice point have a three-peak structure.