Quantum phase transitions in trimerized zig-zag spin ladders

TL;DR

This paper investigates how trimerized modulation affects quantum phase transitions in a spin-1/2 zig-zag ladder, revealing a complex phase diagram with multiple quantum states driven by lattice deformations.

Contribution

It introduces an effective triple sine-Gordon field theory and block-spin perturbation theory to analyze the impact of trimerization on quantum phase transitions.

Findings

Identification of modulation-driven quantum phase transitions.

Discovery of a rich phase diagram including up-up-down and plateau states.

Analysis of the interplay between frustration and exchange modulation.

Abstract

We analyze the effects of a trimerized modulation in a quantum spin $S=\frac12$ zig-zag ladder at the magnetization plateau $M=1/3$. Such periodicity is argued to be stemmed from lattice deformations by phonons. The interplay between frustration and exchange modulation is well described by an effective triple sine-Gordon field theory close to the homogeneous ladder and by block-spin perturbation theory in the weakly coupled trimers regime. The characteristic triple degeneracy of the ground state for homogeneous ladders gives place to modulation driven quantum phase transitions, leading to a rich phase diagram including up-up-down, quantum plateau and gapless plateau states.