Low-energy effective theory and two distinct critical phases in a spin-1/2 frustrated three-leg spin tube

TL;DR

This paper develops a low-energy effective theory for a frustrated spin-1/2 three-leg spin tube, revealing three quantum phases including two gapless phases with distinct conformal central charges, and elucidates their properties through numerical methods.

Contribution

It introduces a novel effective bosonization-based theory for the spin tube and identifies two distinct gapless phases with different central charges, linked to spin frustration effects.

Findings

Identified three ground state phases: one gapped and two gapless.

Discovered the gapless phases have conformal central charges c=1 and 3/2.

Linked the c=3/2 phase to spin frustration and SU(2)k=2 Wess-Zumino-Witten-Novikov universality class.

Abstract

Motivated by the crystal structures of [(CuCl2tachH)3Cl]Cl2 and Ca3Co2O6, we develop a low-energy effective theory using the bosonization technique for a spin-1/2 frustrated three-leg spin tube with trigonal prism units in two limit cases. The features obtained with the effective theory are numerically elucidated by the density matrix renormalization group method. Three different quantum phases in the ground state of the system, say, one gapped dimerized phase and two distinct gapless phases, are identified, where the two gapless phases are found to have the conformal central charge c=1 and 3/2, respectively. Spin gaps, spin and dimer correlation functions, and the entanglement entropy are obtained. In particular, it is disclosed that the critical phase with c=3/2 is the consequence of spin frustrations, which might belong to the SU(2)k=2 Wess-Zumino-Witten-Novikov universality class, and is induced by the twist term in the bosonized Hamiltonian density.