We study the doped and undoped quantum dimer model using exact diagonalization. In the undoped case, previous studies are consistent with the picture that in the region V/J < 0 the ground state is a spin-Peierls state which is four-fold degenerate. We extend the previous calculation and show convincing evidence that a gap exists between the degenerate ground state and the other excitation states. This is further evidence for the spin-Peierls phase. In the doped model, we search for the existence of a stripe phase where the hole-rich region is anisotropic. We introduce a new dimer-hole correlation function, which can indicate the shape of the hole-rich region. Our results show evidence that the holes tend to cluster together with an anisotropic spatial distribution when the holes are not very mobile. But we do not see strong evidence for the existence of a stripe phase.We study the doped and undoped quantum dimer model using exact diagonalization. In the undoped case, previous studies are consistent with the picture that in the region V/J < 0 the ground state is a spin-Peierls state which is four-fold degenerate. We extend the previous calculation and show convincing evidence that a gap exists between the degenerate ground state and the other excitation states. This is further evidence for the spin-Peierls phase. In the doped model, we search for the existence of a stripe phase where the hole-rich region is anisotropic. We introduce a new dimer-hole correlation function, which can indicate the shape of the hole-rich region. Our results show evidence that the holes tend to cluster together with an anisotropic spatial distribution when the holes are not very mobile. But we do not see strong evidence for the existence of a stripe phase.

Jan 1, 20010 citations

Lightly doped dimerized spin chain in the one-dimensional t−J−J′ model

Alexander Seidel, Patrick A. Lee

We study the one-dimensional $t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}$-model in the limit of small hole doping x and small $J/t,$ ${J}^{\ensuremath{'}}/t.$ Special emphasis is put on the regime ${J}^{\ensuremath{'}}/J\ensuremath{\approx}0.5,$ 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 nonintegrable class of models that the charge degrees of freedom behave as noninteracting 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 ${J}^{\ensuremath{'}}/J=0.5$ we construct a variational spin-polaron wave function for the hole and find good agreement with our perturbative results.We study the one-dimensional $t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}$-model in the limit of small hole doping x and small $J/t,$ ${J}^{\ensuremath{'}}/t.$ Special emphasis is put on the regime ${J}^{\ensuremath{'}}/J\ensuremath{\approx}0.5,$ 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 nonintegrable class of models that the charge degrees of freedom behave as noninteracting 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 ${J}^{\ensuremath{'}}/J=0.5$ we construct a variational spin-polaron wave function for the hole and find good agreement with our perturbative results.

arXiv:cond-mat/0309296Physical Review BMar 19, 20045 citations

We study the one-dimensional $t\ensuremath{-}J\ensuremath{-}{J}^{\ensuremath{'}}$-model in the limit of small hole doping x and small

J/t,

${J}^{\ensuremath{'}}/t.$ Special emphasis is put on the regime ${J}^{\ensuremath{'}}/J\ensuremath{\approx}0.5,$ 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 nonintegrable class of models that the charge degrees of freedom behave as noninteracting 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 ${J}^{\ensuremath{'}}/J=0.5$ we construct a variational spin-polaron wave function for the hole and find good agreement with our perturbative results.