Quantum criticality in an asymmetric three-leg spin tube: A strong rung-coupling perspective

Abstract

We study quantum phase transitions in the asymmetric variation of the three-leg Heisenberg tube for half-odd-integer spin, with a modulation of one of the rung exchange couplings $J_{\perp }^{\prime }$ while the other two are kept constant $J_{\perp }$. We focus on the strong rung-coupling regime $J_{\perp }\gg J_{\parallel }$, where $J_{\parallel }$ is the leg coupling, and analyze the effective spin-orbital model with a transverse crystal field in detail. Applying the Abelian bosonization to the effective model, we find that the system is in the dimer phase for the general half-odd-integer-spin cases without the rung modulation; the phase transition between the dimer and Tomonaga-Luttinger-liquid phases induced by the rung modulation is of the SU(2)-symmetric Berezinskii-Kosterlitz-Thouless type. Moreover, we perform a level spectroscopy analysis for the effective model for spin-1/2 using exact diagonalization, to determine the precise transition point $|J_{\perp }^{\prime }-J_{\perp }|/J_{\parallel }\sim 0.283$ in the strong rung-coupling limit. The presence of the dimer phase in a small but finite region is also confirmed by a density-matrix renormalization group calculation on the original spin-tube model.

14 pages, 6 figures

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