Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain

• URL: http://arxiv.org/abs/2302.14090v2
• Date: Mon, 22 May 2023 13:36:36 GMT
• Title: Even-odd effects in the $J_1-J_2$ SU($N$) Heisenberg spin chain
• Authors: Lo\"ic Herviou, Sylvain Capponi, Philippe Lecheminant
• Abstract summary: We show that a fully gapped SU($N$) universality bond solid made of $N$ sites is formed above a critical value of $J/J$ for all $N$. For even $N$, the phase smoothly interpolates to the large $J$ regime where the model can be viewed as a zigzag SU($N$) two-leg spin ladder. In stark contrast to the even case, we show that the $N$-merized phase with odd $N$ only has a finite extent with no incommensuration.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The zero-temperature phase diagram of the $J_1-J_2$ SU($N$) antiferromagnetic Heisenberg spin chain is investigated by means of complementary field theory and numerical approaches for general $N$. A fully gapped 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 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 $N$ only has a finite extent with no incommensuration. A gapless phase in the SU($N$)$_1$ universality class is stabilized for larger $J_2$ that stems from the existence of a massless renormalization group flow from SU($N$)$_2$ to SU($N$)$_1$ conformal field theories when $N$ is odd.

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