Dimerizations in spin-S antiferromagnetic chains with three-spin

We show that spin $S$ Heisenberg spin chains with an additional three-body interaction of the form $({\mathbf{S}}_{\mathbf{i}\mathbf{\ensuremath{-}}\mathbf{1}}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{\mathbf{i}})({\mathbf{S}}_{\mathbf{i}}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{\mathbf{i}+\mathbf{1}})+\mathrm{H}.\mathrm{c}.$ possess fully dimerized ground states if the ratio of the three-body interaction to the bilinear one is equal to $1/[4S(S+1)\ensuremath{-}2]$. This result generalizes the Majumdar-Ghosh point of the ${J}_{1}\ensuremath{-}{J}_{2}$ chain, to which the present model reduces for $S=1/2$ . For $S=1$ , we use the density matrix renormalization group method to show that the transition between the Haldane and the dimerized phases is continuous with a central charge $c=3/2$ . Finally, we show that such a three-body interaction appears naturally in a strong-coupling expansion of the Hubbard model, and we discuss the consequences for the dimerization of actual antiferromagnetic chains.We show that spin $S$ Heisenberg spin chains with an additional three-body interaction of the form $({\mathbf{S}}_{\mathbf{i}\mathbf{\ensuremath{-}}\mathbf{1}}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{\mathbf{i}})({\mathbf{S}}_{\mathbf{i}}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{\mathbf{i}+\mathbf{1}})+\mathrm{H}.\mathrm{c}.$ possess fully dimerized ground states if the ratio of the three-body interaction to the bilinear one is equal to $1/[4S(S+1)\ensuremath{-}2]$. This result generalizes the Majumdar-Ghosh point of the ${J}_{1}\ensuremath{-}{J}_{2}$ chain, to which the present model reduces for $S=1/2$. For $S=1$, we use the density matrix renormalization group method to show that the transition between the Haldane and the dimerized phases is continuous with a central charge $c=3/2$. Finally, we show that such a three-body interaction appears naturally in a strong-coupling expansion of the Hubbard model, and we discuss the consequences for the dimerization of actual antiferromagnetic chains.

arXiv:1110.3394Physical Review LettersMar 20, 201247 citations

Spin-Peierls instability in the spin- 1∕2 Heisenberg three-leg ladder

Mohamed Moussadek Azzouz, Khalada Shahin, Gennady Y. Chitov

Because the three-leg ladder behaves like a renormalized single Heisenberg chain, we argue that a spin-Peierls instability must occur in this system when it is coupled to three-dimensional phonons. Using the bond-mean-field theory, we show that this is indeed the case. The dimerized state below the spin-Peierls transition temperature forms into the columnar dimerized phase instead of the staggered one. This contrasts with the argument based on antiferromagnetism. A physical argument based rather on spin bonding into singlets could explain why the columnar configuration is favored. No quantum criticality (gaplessness) can occur in the columnar arrangement of the dimerized chains.Because the three-leg ladder behaves like a renormalized single Heisenberg chain, we argue that a spin-Peierls instability must occur in this system when it is coupled to three-dimensional phonons. Using the bond-mean-field theory, we show that this is indeed the case. The dimerized state below the spin-Peierls transition temperature forms into the columnar dimerized phase instead of the staggered one. This contrasts with the argument based on antiferromagnetism. A physical argument based rather on spin bonding into singlets could explain why the columnar configuration is favored. No quantum criticality (gaplessness) can occur in the columnar arrangement of the dimerized chains.

arXiv:0708.4181Physical Review BOct 26, 200720 citations

Random antiferromagnetic spin chains with enlarged symmetry

Jos 'e A. Hoyos, E. Miranda

Bulletin of the American Physical SocietyMar 15, 20060 citations

We show that spin

S

Heisenberg spin chains with an additional three-body interaction of the form $({\mathbf{S}}_{\mathbf{i}\mathbf{\ensuremath{-}}\mathbf{1}}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{\mathbf{i}})({\mathbf{S}}_{\mathbf{i}}\ifmmode\cdot\else\textperiodcentered\fi{}{\mathbf{S}}_{\mathbf{i}+\mathbf{1}})+\mathrm{H}.\mathrm{c}.$ possess fully dimerized ground states if the ratio of the three-body interaction to the bilinear one is equal to $1/[4S(S+1)\ensuremath{-}2]$. This result generalizes the Majumdar-Ghosh point of the ${J}_{1}\ensuremath{-}{J}_{2}$ chain, to which the present model reduces for

S=1/2

. For

S=1

, we use the density matrix renormalization group method to show that the transition between the Haldane and the dimerized phases is continuous with a central charge

c=3/2

. Finally, we show that such a three-body interaction appears naturally in a strong-coupling expansion of the Hubbard model, and we discuss the consequences for the dimerization of actual antiferromagnetic chains.