Properties of the spin liquid phase in the vicinity of the N\'eel - Spin-Spiral Lifshitz transition in frustrated magnets

TL;DR

This paper investigates the universal properties of a gapped spin liquid phase emerging near the Lifshitz transition between Ne9el and spin spiral phases in frustrated 2D magnets, combining field theory and numerical methods.

Contribution

It provides a theoretical framework for understanding the spin liquid near the Lifshitz point and compares predictions with numerical series expansion results for a specific model.

Findings

Spin liquid phase is similar to the gapped Haldane phase in 1D.

Critical points and excitation spectra are characterized near the Lifshitz transition.

Numerical results support the field theory predictions.

Abstract

Three decades ago Ioffe and Larkin pointed out a generic mechanism for the formation of a gapped spin liquid. In the case when a classical two-dimensional (2D) frustrated Heisenberg magnet undergoes a Lifshitz transition between a collinear N\'eel phase and a spin spiral phase, quantum effects usually lead to the development of a spin-liquid phase sandwiched between the N\'eel and spin spiral phases. In the present work, using field theory techniques, we study properties of this universal spin liquid phase. We examine the phase diagram near the Lifshitz point and calculate the positions of critical points, excitation spectra, and spin-spin correlations functions. We argue that the spin liquid in the vicinity of 2D Lifshitz point (LP) is similar to the gapped Haldane phase in integer-spin 1D chains. We also consider a specific example of a frustrated system with the spiral-N\'eel LP, the $J_1-J_3$ antiferromagnet on the square lattice that manifests the spin liquid behavior. We present numerical series expansion calculations for this model and compare results of the calculations with predictions of the developed field theory.