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arXiv:cond-mat/0305194 · Physical review. B, Condensed matter

SU(N) evolution of a frustrated spin ladder

M. J. Bhaseen, Alexei M. Tsvelik

Published Sep 5, 2003• 10 citations
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Abstract

Recent studies indicate that the weakly coupled, ${J}_{\ensuremath{\perp}}\ensuremath{\ll}J,$ spin-1/2 Heisenberg antiferromagnet with next-nearest-neighbor frustration, ${J}_{\ifmmode\times\else\texttimes\fi{}},$ supports massive spinons for ${J}_{\ifmmode\times\else\texttimes\fi{}}{=J}_{\ensuremath{\perp}}/2.$ The straightforward $\mathrm{SU}(N)$ generalization of the low-energy ladder Hamiltonian yields two independent $\mathrm{SU}(N)$ Thirring models with $N\ensuremath{-}1$ multiplets of massive ``spinon'' excitations. We study the evolution of the complete set of low energy dynamical structure factors using form factors. Those corresponding to the smooth (staggered) magnetizations are qualitatively different (the same) in the $N=2$ and $N>2$ cases. The absence of single-particle peaks preserves the notion of spinons stabilized by frustration. In contrast to the ladder, we note that the $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ limit of the four chain model is not a trivial free theory.

DOI
10.1103/physrevb.68.094405

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The phase diagram of a frustrated S=1/2 antiferromagnetic spin ladder with additional next-nearest neighbor exchanges, both diagonal and inchain, is studied by a weak-coupling effective field theory approach combined with exact diagonalization for finite systems. In addition to two known phases with rung-singlet and Haldane-type ground states, we observe two new phases with dimerization along the chains. Furthermore, the transitions between the different phases are studied and shown to be either first order or to belong to the universality class of the two-dimensional Ising model. The nature of elementary excitations is discussed briefly.
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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 NNN. A fully gapped SU(N)\mathrm{SU}(N)SU(N) valence bond solid made of NNN sites is formed above a critical value of J2/J1{J}_{2}/{J}_{1}J2​/J1​ for all NNN. We find that the extension of this NNN-merized phase for larger values of J2{J}_{2}J2​ strongly depends on the parity of NNN. For even NNN, the phase smoothly interpolates to the large J2{J}_{2}J2​ regime where the model can be viewed as a zigzag SU(N)\mathrm{SU}(N)SU(N) two-leg spin ladder. The phase exhibits both a NNN-merized ground state and incommensurate spin-spin correlations. In stark contrast to the even case, we show that the NNN-merized phase with odd NNN has only a finite extent with no incommensuration. A gapless phase in the SU(N)1\mathrm{SU}{(N)}_{1}SU(N)1​ universality class is stabilized for larger J2{J}_{2}J2​ that stems from the existence of a massless renormalization group flow from SU(N)2\mathrm{SU}{(N)}_{2}SU(N)2​ to SU(N)1\mathrm{SU}{(N)}_{1}SU(N)1​ conformal field theories when NNN is odd.