Physics – Condensed Matter – Strongly Correlated Electrons
Scientific paper
2012-01-10
Physics
Condensed Matter
Strongly Correlated Electrons
6 pages, 4 figures
Scientific paper
Excitation spectra of $S=1/2$ and S=1 frustrated Heisenberg antiferromagnetic chains with bond alternation (explicit dimerization) are studied, by a combination of analytical and numerical methods. The system undergoes a dimerization transition at a critical bond alternation parameter $\delta=\delta_{\rm c}$, where $\delta_{\rm c} = 0$ for the $S=1/2$ chain. Except at the transition, the SU(2) symmetric sine-Gordon theory is known to be an effective field theory of the system. The sine-Gordon theory has a SU(2)- triplet and a SU(2) singlet of elementary excitation, and the mass ratio $r$ of the singlet to the triplet is $\sqrt{3}$. However, our numerical calculation with the infinite time-evolving block decimation method shows that $r$ depends on the frustration (next-nearest neighbor coupling) and is generally different from $\sqrt{3}$. This can be understood as an effect of marginal perturbation to the sine-Gordon theory. In fact, at the critical frustration separating the second-order and first-order dimerization transitions, the marginal operator vanishes and $r=\sqrt{3}$ holds. We derive the mass ratio $r$ analytically using form-factor perturbation theory combined with a renormalization-group analysis. Our formula agrees well with the numerical results, confirming the theoretical picture. The present theory also implies that, in the very vicinity of the second-order dimerization critical point, the mass ratio approaches to $\sqrt{3}$. However, such region is extremely small and would be difficult to observe numerically.
Oshikawa Masaki
Takayoshi Shintaro
No associations
LandOfFree
Mass ratio of elementary excitations in frustrated antiferromagnetic chains with dimerization does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Mass ratio of elementary excitations in frustrated antiferromagnetic chains with dimerization, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Mass ratio of elementary excitations in frustrated antiferromagnetic chains with dimerization will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-462598