A Panoply of Orders from a Quantum Lifshitz Field Theory

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.

5 pages, 3 figures, supplement (5 pages)

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Cited by in corpus (27)

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• Spin dynamics in the high-field phases of volborthite
• Frustrated spin chain physics near the Majumdar-Ghosh point in szenicsite Cu${}_3$(MoO${}_4$)(OH)${}_4$
• Multipolar phase in frustrated spin-1/2 and 1 chains
• Presaturation phase with no dipolar order in a quantum ferro-antiferromagnet
• Field-driven quantum phase transitions in $S=1/2$ spin chains
• Magnetic phase diagram of the strongly frustrated quantum spin chain system PbCuSO${}_4$(OH)${}_2$ in tilted magnetic fields
• Linarite - a quasi-critical J${}_1$-J${}_2$ chain
• The magnetic phase diagram of the frustrated spin chain compound linarite, PbCuSO${}_4$(OH)${}_2$, as seen by neutron diffraction and ${}^1$H-NMR
• Collinear Spin-density-wave Order and Anisotropic Spin Fluctuations in the Frustrated $J_1$--$J_2$ Chain Magnet NaCuMoO${}_4$(OH)
• Highly dispersive magnons with spin-gap like features in the frustrated ferromagnetic S=1/2 chain compound Ca2Y2Cu5O10 detected by inelastic neutron scattering
• The origin of up-up-down-down magnetic order in Cu${}_2$GeO${}_4$
• Semiclassical analysis of a magnetization plateau in a 2D frustrated ferrimagnet
• Magnetoelastic study on the frustrated quasi-one-dimensional spin-1/2 magnet LiCuVO${}_4$
• Dynamics of Bound Magnon Pairs in the Quasi-One-Dimensional Frustrated Magnet LiCuVO_4
• Properties of the spin liquid phase in the vicinity of the Néel - Spin-Spiral Lifshitz transition in frustrated magnets
• Effects of Dzyaloshinskii-Moriya interactions in volborthite: Magnetic orders and thermal Hall effect
• Low-energy spin excitations of the frustrated ferromagnetic $J_1$-$J_2$ chain material linarite, PbCuSO${}_4$(OH)${}_2$, in applied magnetic fields $\mathbf{H}\parallel b$ axis
• Field induced non-BEC transitions in frustrated magnets
• Quantum Lifshitz points in an altermagnetic metal
• Emergent incommensurate correlations in the frustrated ferromagnetic spin-1 chains
• Quantum Lifshitz criticality in a frustrated two-dimensional XY model
• Colossal quasiparticle radiation in the Lifshitz spin liquid phase of a two-dimensional quantum antiferromagnet
• Spin-orbit coupled bosons in one dimension: emergent gauge field and Lifshitz transition