Cubic interactions and quantum criticality in dimerized antiferromagnets

Abstract

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

High-order study of the quantum critical behavior of a frustrated spin- 12 antiferromagnet on a stacked honeycomb bilayer

“…[16,17]) yield (J ′ /J) c ≈ 1.48. In the Shastry-Sutherland material SrCu 2 (BO 3 ) 2 , for which (J ′ /J) ≈ 1.6, the triplon crystalline phases show up as a series of magnetization plateaux at unconventional filling fractions [11,12] that are stabilized by complex manybody interactions among the triplons [9,12,18,19]. Indeed, the magnetization plateaux in SrCu 2 (BO 3 ) 2 at low magnetization are now quite well understood in terms of triplon bound states [20,21].…”

“…[9]). The first two, each with two sites per unit cell, both have the dimer J ′ bonds parallel (say, along the row direction of the square lattice).…”

Spin excitations in the two-dimensional strongly coupled dimer system malachite

“…1a) displays a conventional quantum critical point (QCP), the staggered dimer lattice (Fig. 1b) has a QCP with dangerously irrelevant Berry-terms [15].Experimental realizations of systems that could confirm these theoretical ideas are scarce. In this Article, we have studied the magnetic excitations in the mineral malachite, which realizes a variant of the staggered dimer lattice, where half of the interdimer couplings perpendicular to the dimers are removed (see Fig.…”

“…However, it was recently shown that certain classes of non-frustrated 2D coupled dimers develop non-trivial cubic interactions of purely quantum mechanical origin that lead to simultaneous condensation of the one-triplon and two-triplon excitations at the Γ-point at the critical interdimer coupling strength [15]. These three-particle interactions have been shown to correspond to Berry-phase terms in the O(3) non-linear σ-model [15] and lead to the equivalent of vector boson excitations in the adjacent Néel phase [16]. The geometry of the dimer lattice has been shown to be crucial: While the columnar dimer lattice (Fig.…”

“…Similar to the staggered dimer lattice, the dimers in this depleted staggered dimer lattice are coupled in an asymmetric fashion, which leads to a QCP with emergent antiferromagnetism at the Γ-point k = 0. The malachite coupling scheme therefore falls in the category of models where Berry-phase terms may be important at the QCP [15]. arXiv:1412.5908v1 [cond-mat.str-el]…”