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 ′ ⊥ while the other two are kept constant J ⊥ . We focus on the strong rung-coupling regime J ⊥ ≫ J , where J 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 ′ ⊥ − J ⊥ |/J ∼ 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.

Ground State Phase Diagram of Twisted Three-Leg Spin Tube in Magnetic Field

“…where τ + j (τ − j ) represents the raising (lowering) operator acting on the two chirality states |τ z = +1/2 and |τ z = −1/2 of the unit triangle at j-th site, and S j is spin- 1 2 operator of the same unit triangle. 5,7,8,25) Below the magnetization plateau, the bosonization analysis shows that the spin and chirality degrees of freedoms are separated within a perturbation analysis with respect to the second term in Eq. 5.…”

Quantum order by disorder in Frustrated Spin Nanotubes

“…1). Motivated by the discovery of frustrated spin chain materials [37][38][39][40], spin nanotubes have been previously studied with different couplings and boundary conditions, both with and without magnetic field [41][42][43][44][45][46]. Spin nanotubes can also be regarded as nleg spin ladders with periodic boundary conditions along the short direction and we point out similarities and differences to previous studies of these systems [47][48][49][50][51][52][53][54][55].…”