Geometrically Frustrated Anisotropic Four-Leg Spin-$1/2$ Nanotube

TL;DR

This paper uses a real space quantum renormalization group approach to analyze a frustrated anisotropic four-leg spin-1/2 nanotube, revealing phase transitions, critical points, and magnetization behavior, with numerical validation.

Contribution

It introduces a novel QRG method to study the phase diagram and critical phenomena of a frustrated spin nanotube, including mapping to a 1D XXZ chain and analyzing magnetization plateaus.

Findings

Diagonal frustration is marginal and does not alter universality class.

Strong leg coupling leads to a weakly interacting plaquette limit.

Magnetization curves and phase transition points are significantly affected by anisotropy.

Abstract

We develop a real space quantum renormalization group (QRG) to explore a frustrated anisotropic four-leg spin-1/2 nanotube in the thermodynamic limit. We obtain the phase diagram, fixed points, critical points, the scaling of coupling constants and magnetization curves. Our investigation points out that in the case of strong leg coupling the diagonal frustrating interaction is marginal under QRG transformations and does not affect the universality class of the model. Remarkably, the renormalization equations express that the spin nanotube prepared in the strong leg coupling case goes to the strong plaquette coupling limit (weakly interacting plaquettes). Subsequently, in the limit of weakly interacting plaquettes, the model is mapped onto a 1D spin-1/2 XXZ chain in a longitudinal magnetic field under QRG transformation. Furthermore, the effective Hamiltonian of the spin nanotube inspires both first and second order phase transitions accompanied by the fractional magnetization plateaus. Our results show that the anisotropy changes the magnetization curve and the phase transition points, significantly. Finally, we report the numerical exact diagonalization results to compare the ground state phase diagram with our analytical visions.