Lightly doped dimerized spin chain in the one-dimensional t-J-J' model

Abstract

We study the one-dimensional t-J-J'-model in the limit of small hole doping $x$ and small $J/t$, $J^{\prime }/t$. Special emphasis is put on the regime $J^{\prime }/J\approx .5$ where a spin gap is present at small doping and the undoped spin chain is strongly dimerized. Using a perturbative approach and Luttinger liquid arguments, we demonstrate for this non-integrable class of models that the charge degrees of freedom behave as non-interacting spinless solitons in the dilute hole limit. Our approach is also used to evaluate the energy and mass renormalization of a single hole. Interestingly, the corrections of these quantities are in powers of $\sqrt{J/t}$. At $J^{\prime }/J=.5$ we construct a variational spin-polaron wave function for the hole and find good agreement with our perturbative results.

13 pages, 5 figures, published version, new title and minor changes

References in corpus (2)

• S=1/2 chains and spin-Peierls transition in TiOCl
• Quantal phases, disorder effects and superconductivity in spin-Peierls systems

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• Optical study of orbital excitations in transition-metal oxides
• Flux period, spin gap, and pairing in the one-dimensional t-J-J'-model
• Linking infinite bond-dimension matrix product states with frustration-free Hamiltonians