Even-odd effects in the J1−J2 SU(N) Heisenberg spin chain

Abstract

The zero-temperature phase diagram of the ${J}_{1}\text{\ensuremath{-}}{J}_{2}\phantom{\rule{4pt}{0ex}}\mathrm{SU}(N)$ antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general $N$. A fully gapped $\mathrm{SU}(N)$ valence bond solid made of $N$ sites is formed above a critical value of ${J}_{2}/{J}_{1}$ for all $N$. We find that the extension of this $N$-merized phase for larger values of ${J}_{2}$ strongly depends on the parity of $N$. For even $N$, the phase smoothly interpolates to the large ${J}_{2}$ regime where the model can be viewed as a zigzag $\mathrm{SU}(N)$ two-leg spin ladder. The phase exhibits both a $N$-merized ground state and incommensurate spin-spin correlations. In stark contrast to the even case, we show that the $N$-merized phase with odd $N$ has only a finite extent with no incommensuration. A gapless phase in the $\mathrm{SU}{(N)}_{1}$ universality class is stabilized for larger ${J}_{2}$ that stems from the existence of a massless renormalization group flow from $\mathrm{SU}{(N)}_{2}$ to $\mathrm{SU}{(N)}_{1}$ conformal field theories when $N$ is odd.