Fractionalized Z2 Classical Heisenberg Spin Liquids

Abstract

Quantum spin systems are by now known to exhibit a large number of different classes of spin liquid phases. By contrast, for classical Heisenberg models, only one kind of fractionalised spin liquid phase, the so-called Coulomb or U (1) spin liquid, has until recently been identified: this exhibits algebraic spin correlations and impurity moments, 'orphan spins', whose size is a fraction of that of the underlying microscopic degrees of freedom. Here, we present two Heisenberg models exhibiting fractionalisation in combination with exponentially decaying correlations. These can be thought of as a classical continuous spin version of a Z2 spin liquid. Our work suggests a systematic search and classification of classical spin liquids as a worthwhile endeavour. PACS numbers:Fractionalisation is one of the several unusual properties generally observed in systems evading low temperature conventional symmetry breaking ordered states in favor of unconventional topological orders. On account of such exotic behavior, much attention has been devoted to the identification of systems exhibiting such new topological physics. Frustrated magnets [1][2][3] have played a prominent role, where several spin liquids (SL) [4,5] starting in the late 90s [6] were identified [7][8][9].While by now a multitude of quantum SL have been discovered [10] and classified [11], the situation with classical Heisenberg SL is comparatively much sparser. The first Heisenberg spin liquid to be identified unambiguously, the antiferromagnet on the pyrochlore lattice [7,12] is a U (1) spin liquid exhibiting pinch-points in its structure factor indicating algebraically decaying correlations [7,[12][13][14][15], as well as fractionalisation of its microscopic degrees of freedom: disorder in the form of dilution creates new, weakly-interacting, magnetic degrees of freedom which possess a half of the microscopic magnetic moments of the Heisenberg model [16,17].Such fractionalisation is perhaps the cleanest signature of spin-liquidity in such a classical setting, as definitions in terms of topological field theory are frustrated by the bulk gapless excitations due to the continuous classical nature of the Heisenberg spins.Given the by now overwhelming variety of known quantum spin liquids (for an example, see Ref. 18), it may therefore come as a surprise that no corresponding richness appears to exist for classical Heisenberg magnets: the U (1) case is the only one studied in detail. It turns up in many settings, such as the checkerboard and pyrochlore lattices (for n = 2 component spins) [7,12], the kagome (for n > 3 component spins) [19,20], or the SCGO 'pyrochlore slab' [21].Here we ask the question whether this absence of evidence of other types of spin liquid is evidence of absence. The answer is that there is indeed more diversity than has been so far recognised: we identify a new SL class which and a kagome (right) lattices. These can be respectively seen as fully connected squares forming a kagome, and fully connected hexagons forming a triangular, la...

Degenerate and chiral states in the extended Heisenberg model on the kagome lattice

“…For h = 0, as commented in Ref. [18], there are no peaks indicating that there is not thermal selection and no "pinchpoints", consistent with a non-algebraic spin liquid phase scenario. We show as a typical example at h/J 1 = 4 the component perpendicular to the magnetic field in Fig.…”

“…Of particular interest in the phase diagram are the points dubbed HFP1 (Highly Frustraded Point), which is the well known first nearest neighbors model, and corresponds to corner sharing triangles, and HFP2, corresponding to corner sharing hexagons, studied in Ref. [18]. Although apparently similar, the low temperature physics of these two maximally frustrated points in the kagome lattice is quite different.…”

Characterization of quantum spin liquids and their spinon band structures via functional renormalization

“…Later, the observation of the fractional quantum Hall effect in two-dimensional electron gases marked the experimental breakthrough in this growing research area [5][6][7]. Lately, fractionalization has attracted increasing interest in the context of magnetic systems where, among other examples [8,9], it manifests through monopole excitations in classical spin ice systems [10][11][12][13] or through spinons in spin-1/2 quantum spin liquids [14,15].…”

Orphan Spins in the S=52 Antiferromagnet CaFe2O4Stock1, Rodriguez2, Lee3 et al. 2017Phys. Rev. Lett.204480View full textAdd to dashboardCite

“…The presence of static boundaries separating A and B order parameters brings the possibility of magnetic states that have different properties from the bulk, termed orphan spins. [31][32][33] We apply neutron diffraction and inelastic scattering to identify and characterize these states. Further experimental details are provided in the supplementary information.…”