We investigate the quantum Heisenberg model on the pyrochlore lattice for a generic spin S in the presence of nearest-neighbor J1 and second-nearest-neighbor J2 exchange interactions. By employing the pseudofermion functional renormalization group method, we find, for S = 1/2 and S = 1, an extended quantum-spin-liquid phase centered around J2 = 0, which is shown to be robust against the introduction of breathing anisotropy. The effects of temperature, quantum fluctuations, breathing anisotropies, and a J2 coupling on the nature of the scattering profile, and the pinch points, in particular, are studied. For the magnetic phases of the J1-J2 model, quantum fluctuations are shown to renormalize phase boundaries compared to the classical model and to modify the ordering wave vectors of spiral magnetic states, while no new magnetic orders are stabilized. arXiv:1802.09546v3 [cond-mat.str-el] 9 Jan 2019 J 2 / J 1 = 0.22 J 2 / J 1 = 0.13 J 2 / J 1 = 0.06 J 2 / J 1 = 0 J 2 / J 1 = − 0.06 J 2 / J 1 = − 0.13 J 2 / J 1 = − 0.22

We investigate the quantum phases of the frustrated spin-$\frac{1}{2}$ $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice with ferromagnetic $J_1$ and antiferromagnetic $J_2$ and $J_3$ interactions. Using the pseudo-fermion functional renormalization group technique, we find an intermediate paramagnetic phase located between classically ordered ferromagnetic, stripy antiferromagnetic, and incommensurate spiral phases. We observe that quantum fluctuations lead to significant shifts of the spiral pitch angles compared to the classical limit. By computing the response of the system with respect to various spin rotation and lattice symmetry-breaking perturbations, we identify a complex interplay between different nematic spin states in the paramagnetic phase. While retaining time-reversal invariance, these phases either break spin-rotation symmetry, lattice-rotation symmetry, or a combination of both. We therefore propose the $J_1$-$J_2$-$J_3$ Heisenberg model on the square lattice as a paradigmatic example where different intimately connected types of nematic orders emerge in the same model.Comment: Published version. 8 pages, 5 figure

We address the long-standing problem of the microscopic origin of the richly diverse phenomena in the chromium breathing pyrochlore material family. Combining electronic structure and renormalization group techniques we resolve the magnetic interactions and analyze their reciprocal-space susceptibility. We show that the physics of these materials is principally governed by long-range Heisenberg Hamiltonian interactions, a hitherto unappreciated fact. Our calculations uncover that in these isostructural compounds, the choice of chalcogen triggers a proximity of the materials to classical spin liquids featuring degenerate manifolds of wave-vectors of different dimensions: A Coulomb phase with three-dimensional degeneracy for LiInCr 4 O 8 and LiGaCr 4 O 8 , a spiral spin liquid with two-dimensional degeneracy for CuInCr 4 Se 8 and one-dimensional line degeneracies characteristic of the face-centered cubic antiferromagnet for LiInCr 4 S 8 , LiGaCr 4 S 8 and CuInCr 4 S 8 . The surprisingly complex array of prototypical pyrochlore behaviors we discovered in chromium spinels may inspire studies of transition paths between different semi-classical spin liquids by doping or pressure.

A spin-1 Heisenberg model on trimerized Kagomé lattice is studied by doing a low-energy bosonic theory in terms of plaquette-triplons defined on its triangular unit-cells. The model considered has an intra-triangle antiferromagnetic exchange interaction, J (set to 1), and two inter-triangle couplings, J > 0 (nearest-neighbor) and J (next-nearest-neighbor; of both signs). The triplon analysis performed on this model investigates the stability of the trimerized singlet ground state (which is exact in the absence of inter-triangle couplings) in the J -J plane. It gives a quantum phase diagram that has two gapless antiferromagnetically ordered phases separated by the spin-gapped trimerized singlet phase. The trimerized singlet ground state is found to be stable on J = 0 line (the nearest-neighbor case), and on both sides of it for J = 0, in an extended region bounded by the critical lines of transition to the gapless antiferromagnetic phases. The gapless phase in the negative J region has a coplanar 120• -antiferromagnetic order with √ 3 × √ 3 structure. In this phase, all the magnetic moments are of equal length, and the angle between any two of them on a triangle is exactly 120• . The magnetic lattice in this case has a unit-cell consisting of three triangles. The other gapless phase, in the positive J region, is found to exhibit a different coplanar antiferromagnetic order with ordering wavevector q = (0, 0). Here, two magnetic moments in a triangle are of same magnitude, but shorter than the third. While the angle between two short moments is 120• − 2δ, it is 120• + δ between a short and the long one. Only when J = J , their magnitudes become equal and the relative-angles 120• . The magnetic lattice in this q = (0, 0) phase has the translational symmetry of the Kagomé lattice with triangular unit-cells of reduced (isosceles) symmetry. This reduction in the point-group symmetry is found to show up as a difference in the intensities of certain Bragg peaks, whose ratio, I (1,0) /I (0,1) = 4 sin 2 ( π 6 + δ), presents an experimental measure of the deviation, δ, from the 120• order.

We investigate the spin S = 1/2 Heisenberg model on the body centered cubic lattice in the presence of ferromagnetic and antiferromagnetic nearest-neighbor J1, second-neighbor J2, and third-neighbor J3 exchange interactions. The classical ground state phase diagram obtained by a Luttinger-Tisza analysis is shown to host six different (noncollinear) helimagnetic orders in addition to ferromagnetic, Néel, stripe and planar antiferromagnetic orders. Employing the pseudofermion functional renormalization group (PFFRG) method for quantum spins (S = 1/2) we find an extended nonmagnetic region, and significant shifts to the classical phase boundaries and helimagnetic pitch vectors caused by quantum fluctuations while no new long-range dipolar magnetic orders are stabilized. The nonmagnetic phase is found to disappear for S = 1. We calculate the magnetic ordering temperatures from PFFRG and quantum Monte Carlo methods, and make comparisons to available data. arXiv:1902.01179v1 [cond-mat.str-el]