A Panoply of Orders from a Quantum Lifshitz Field Theory

TL;DR

This paper introduces a universal non-linear sigma model for one-dimensional frustrated ferromagnets near a quantum Lifshitz point, revealing complex phase structures and transitions, including a cascade of multipolar phases.

Contribution

It develops a novel field theory framework that captures the rich phase diagram and critical phenomena of frustrated ferromagnets near the Lifshitz point, with analytical insights into their behavior.

Findings

Identification of a metamagnetic transition line to a vector chiral phase

Discovery of a cascade of multipolar phases from a critical endpoint

Asymptotic solubility of the field theory near the Lifshitz point

Abstract

We propose a universal non-linear sigma model field theory for one dimensional frustrated ferromagnets, which applies in the vicinity of a "quantum Lifshitz point", at which the ferromagnetic state develops a spin wave instability. We investigate the phase diagram resulting from perturbations of the exchange and of magnetic field away from the Lifshitz point, and uncover a rich structure with two distinct regimes of different properties, depending upon the value of a marginal, dimensionless, parameter of the theory. In the regime relevant for one dimensional systems with low spin, we find a metamagnetic transition line to a vector chiral phase. This line terminates in a critical endpoint from which emerges a cascade of multipolar phases. We show that the field theory has the property of "asymptotic solubility", so that a particular saddle point approximation becomes asymptotically exact near the Lifshitz point. Our results provide an analytic framework for prior numerical results on frustrated ferromagnets, and can be applied much more broadly.