Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism

TL;DR

This paper investigates a frustrated four-leg spin tube under a magnetic field, revealing a nonmagnetic, factorizable ground state with quantized magnetization differences, using multiple theoretical and numerical methods.

Contribution

It demonstrates the emergence of a factorizable ground state with hidden ferromagnetism in a frustrated spin tube, combining order by disorder and strong-coupling analysis.

Findings

Ground state is nonmagnetic and factorizable in magnetization plateaus.

Quantized relative magnetizations between sublattices.

Ground state shows near-perfect factorization.

Abstract

The interplay between frustration and quantum fluctuation in magnetic systems is known to be the origin of many exotic states in condensed matter physics. In this paper, we consider a frustrated four-leg spin tube under a magnetic field. This system is a prototype to study the emergence of a nonmagnetic ground state factorizable into local states and the associated order parameter without quantum fluctuation, that appears in a wide variety of frustrated systems. The one-dimensional nature of the system allows us to apply various techniques: a path-integral formulation based on the notion of order by disorder, strong-coupling analysis where magnetic excitations are gapped, and density-matrix renormalization group. All methods point toward an interesting property of the ground state in the magnetization plateaus, namely, a quantized value of relative magnetizations between different sublattices (spin imbalance) and an almost perfect factorization of the ground state.