Fractons are topological quasiparticles with limited mobility. While there exists a variety of models hosting these excitations, typical fracton systems require rather complicated many-particle interactions. Here, we discuss fracton behavior in the m
ore common physical setting of classical kagome spin models with frustrated two-body interactions only. We investigate systems with different types of elementary spin degrees of freedom (three-state Potts, XY, and Heisenberg spins) which all exhibit characteristic subsystem symmetries and fracton-like excitations. The mobility constraints of isolated fractons and bound fracton pairs in the three-state Potts model are, however, strikingly different compared to the known type-I or type-II fracton models. One may still explain these properties in terms of type-I fracton behavior and construct an effective low-energy tensor gauge theory when considering the system as a 2D cut of a 3D cubic lattice model. Our extensive classical Monte-Carlo simulations further indicate a crossover into a low temperature glassy phase where the system gets trapped in metastable fracton states. Moving on to XY spins, we find that in addition to fractons the system hosts fractional vortex excitations. As a result of the restricted mobility of both types of defects, our classical Monte-Carlo simulations do not indicate a Kosterlitz-Thouless transition but again show a crossover into a glassy low-temperature regime. Finally, the energy barriers associated with fractons vanish in the case of Heisenberg spins, such that defect states may continuously decay into a ground state. These decays, however, exhibit a power-law relaxation behavior which leads to slow equilibration dynamics at low temperatures.
Quantum spin liquids are long-range entangled phases whose magnetic correlations are determined by strong quantum fluctuations. While an overarching principle specifying the precise microscopic coupling scenarios for which quantum spin-liquid behavio
r arises is unknown, it is well-established that they are preferably found in spin systems where the corresponding classical limit of spin magnitudes $Srightarrowinfty$ exhibits a macroscopic ground state degeneracy, so-called classical spin liquids. Spiral spin liquids represent a special family of classical spin liquids where degenerate manifolds of spin spirals form closed contours or surfaces in momentum space. Here, we investigate the potential of spiral spin liquids to evoke quantum spin-liquid behavior when the spin magnitude is tuned from the classical $Srightarrowinfty$ limit to the quantum $S=1/2$ case. To this end, we first use the Luttinger-Tisza method to formulate a general scheme which allows one to construct new spiral spin liquids based on bipartite lattices. We apply this approach to the two-dimensional square lattice and the three-dimensional hcp lattice to design classical spiral spin-liquid phases which have not been previously studied. By employing the pseudofermion functional renormalization group (PFFRG) technique we investigate the effects of quantum fluctuations when the classical spins are replaced by quantum $S=1/2$ spins. We indeed find that extended spiral spin-liquid regimes change into paramagnetic quantum phases possibly realizing quantum spin liquids. Remnants of the degenerate spiral surfaces are still discernible in the momentum-resolved susceptibility, even in the quantum $S=1/2$ case. In total, this corroborates the potential of classical spiral spin liquids to induce more complex non-magnetic quantum phases.
Motivated by the recent synthesis of the spin-1 A-site spinel NiRh$_{text 2}$O$_{text 4}$, we investigate the classical to quantum crossover of a frustrated $J_1$-$J_2$ Heisenberg model on the diamond lattice upon varying the spin length $S$. Applyin
g a recently developed pseudospin functional renormalization group (pf-FRG) approach for arbitrary spin-$S$ magnets, we find that systems with $S geq 3/2$ reside in the classical regime where the low-temperature physics is dominated by the formation of coplanar spirals and a thermal (order-by-disorder) transition. For smaller local moments $S$=1 or $S$=1/2 we find that the system evades a thermal ordering transition and forms a quantum spiral spin liquid where the fluctuations are restricted to characteristic momentum-space surfaces. For the tetragonal phase of NiRh$_{text 2}$O$_{text 4}$, a modified $J_1$-$J_2^-$-$J_2^perp$ exchange model is found to favor a conventionally ordered Neel state (for arbitrary spin $S$) even in the presence of a strong local single-ion spin anisotropy and it requires additional sources of frustration to explain the experimentally observed absence of a thermal ordering transition.
We investigate the effects of Dzyaloshinsky-Moriya (DM) interactions on the frustrated $J_1$-$J_2$ kagome-Heisenberg model using the pseudo-fermion functional-renormalization-group (PFFRG) technique. In order to treat the off-diagonal nature of DM in
teractions, we develop an extended PFFRG scheme. We benchmark this approach in parameter regimes that have previously been studied with other methods and find good agreement of the magnetic phase diagram. Particularly, finite DM interactions are found to stabilize all types of non-collinear magnetic orders of the $J_1$-$J_2$ Heisenberg model ($mathbf{q}=0$, $sqrt{3}timessqrt{3}$, and cuboc orders) and shrink the extents of magnetically disordered phases. We discuss our results in the light of the mineral {it herbertsmithite} which has been experimentally predicted to host a quantum spin liquid at low temperatures. Our PFFRG data indicates that this material lies in close proximity to a quantum critical point. In parts of the experimentally relevant parameter regime for {it herbertsmithite}, the spin-correlation profile is found to be in good qualitative agreement with recent inelastic-neutron-scattering data.
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling $K_2$, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iri
date Na$_2$IrO$_3$, and may also play a role in $alpha$-RuCl$_3$ and Li$_2$IrO$_3$. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na$_2$IrO$_3$. Moreover, the minimal $K_1$-$K_2$ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.
