Quantum phase transition by cyclic fourspin exchange interaction for S=1/2 twoleg spin ladder
Abstract
We investigate an $S=1/2$ twoleg spin ladder with a cyclic fourspin exchange interaction whose interaction constant is denoted by $J_4$, by using the density matrix renormalization group method. The interchain and the intrachain interaction constant are denoted by $J_{rung}$ and $J_{\rm leg}$, respectively and assumed to be antiferromagnetic. It turns out that a spin gap between the singlet ($S_{tot}^z=0$) and the triplet ($S_{tot}^z=1$) states vanishes at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$. This result is in contrast with the fact that the $S=1/2$ antiferromagnetic Heisenberg ladder, that is the case of $J_{rung} \neq J_{leg}, J_4=0$, has a spin gap for all nonzero value of interchain interaction $J_{\rm rung}>0$. We find a larger value of the correlation length for the spinpair correlation function than a linear size $L$ of the system at $J_4/J_{\rm leg}=0.3$ and $J_{rung}=J_{leg}$: the correlation length $\xi$ is about 204 times of the lattice constant for L=84 for these values of interactions. We also find that the string correlation function decays rather algebraically than exponentially at $J_4/J_{leg}=0.3$ and $J_{rung}=J_{leg}$. These results suggest that there is a quantum phase transition at $J_4/J_{leg} \simeq 0.3$ for $J_{rung}=J_{leg}$. We estimate a phase boundary where the spin gap vanishes in a $J_4/J_{leg}J_{rung}/J_{leg}$ plane and obtain a consistent result with that by a perturbation theory for $J_{\rm rung}/J_{leg}>1$.
 Publication:

arXiv eprints
 Pub Date:
 June 2001
 arXiv:
 arXiv:condmat/0106426
 Bibcode:
 2001cond.mat..6426H
 Keywords:

 Condensed Matter  Statistical Mechanics;
 Condensed Matter  Materials Science
 EPrint:
 12 pages, 14 figures