Quantum spin nanotubes -- frustration, competing orders and criticalities

TL;DR

This paper reviews theoretical studies on spin nanotubes, especially the three-leg spin tube, highlighting their unique quantum phases, phase transitions, and magnetic phenomena, supported by analytical and numerical methods.

Contribution

It provides a comprehensive analysis of the quantum phases, criticalities, and magnetic-field-induced phenomena in spin nanotubes, emphasizing new mechanisms and experimental relevance.

Findings

Spin gap in regular-triangle spin tubes with large rung interaction.

Quantum phase transition to a gapless spin liquid due to lattice distortion.

Magnetic-field-induced phenomena including Neel, dimer, chiral, and inhomogeneous orders.

Abstract

Recent developments of theoretical studies on spin nanotubes are reviewed, especially focusing on the $S=1/2$ three-leg spin tube. In contrast to the three-leg spin ladder, the tube has a spin gap in case of the regular-triangle unit cellwhen the rung interaction is sufficiently large. The effective theory based on the Hubbard Hamiltonian indicates a quantum phase transition to the gapless spin liquid due to the lattice distortion to an isosceles triangle. This is also supported by the numerical diagonalization and the density matrix renormalization group analyses. Furthermore, combining analytical and numerical approaches, we reveal several novel magnetic-field-induced phenomena: N\'eel, dimer, chiral and/or inhomogeneous orders, new mechanism for the magnetization plateau formation,and others. The recently synthesized spin tube materials are also briefly introduced.