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Register a new userThe view of TK-SVM on the phase hierarchy in the classical kagome Heisenberg antiferromagnet
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We illustrate how the tensorial kernel support vector machine (TK-SVM) can probe the hidden multipolar orders and emergent local constraint in the classical kagome Heisenberg antiferromagnet. We show that TK-SVM learns the finite-temperature phase diagram in an unsupervised way. Moreover, in virtue of its strong interpretability, it identifies the tensorial quadrupolar and octupolar orders, which define a biaxial $D_{3h}$ spin nematic, and the local constraint that underlies the selection of coplanar states. We then discuss the disorder hierarchy of the phases, which can be inferred from both the analytical order parameters and a SVM bias parameter. For completeness we mention that the machine also picks up the leading $sqrt{3} times sqrt{3}$ correlations in the dipolar channel at very low temperature, which are however weak compared to the quadrupolar and octupolar orders. Our work shows how TK-SVM can facilitate and speed up the analysis of classical frustrated magnets.
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We perform an extensive density matrix renormalization group (DMRG) study of the ground-state phase diagram of the spin-1/2 J_1-J_2 Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J_2=0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J_2approx 0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J_2 the ground state displays signatures of the magnetic order of the sqrt{3}timessqrt{3} and the q=0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q=0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.
We determine dynamical response functions of the S=1/2 Heisenberg quantum antiferromagnet on the kagome lattice based on large-scale exact diagonalizations combined with a continued fraction technique. The dynamical spin structure factor has important spectral weight predominantly along the boundary of the extended Brillouin zone and energy scans reveal broad response extending over a range of 2 sim 3J concomitant with pronounced intensity at lowest available energies. Dispersive features are largely absent. Dynamical singlet correlations -- which are relevant for inelastic light probes -- reveal a similar broad response, with a high intensity at low frequencies omega/J lesssim 0.2J. These low energy singlet excitations do however not seem to favor a specific valence bond crystal, but instead spread over many symmetry allowed eigenstates.
We study the properties of the Heisenberg antiferromagnet with spatially anisotropic nearest-neighbour exchange couplings on the kagome net, i.e. with coupling J in one lattice direction and couplings J along the other two directions. For J/J > 1, this model is believed to describe the magnetic properties of the mineral volborthite. In the classical limit, it exhibits two kinds of ground states: a ferrimagnetic state for J/J < 1/2 and a large manifold of canted spin states for J/J > 1/2. To include quantum effects self-consistently, we investigate the Sp(N) symmetric generalisation of the original SU(2) symmetric model in the large-N limit. In addition to the dependence on the anisotropy, the Sp(N) symmetric model depends on a parameter kappa that measures the importance of quantum effects. Our numerical calculations reveal that in the kappa-J/J plane, the system shows a rich phase diagram containing a ferrimagnetic phase, an incommensurate phase, and a decoupled chain phase, the latter two with short- and long-range order. We corroborate these results by showing that the boundaries between the various phases and several other features of the Sp(N) phase diagram can be determined by analytical calculations. Finally, the application of a block-spin perturbation expansion to the trimerised version of the original spin-1/2 model leads us to suggest that in the limit of strong anisotropy, J/J >> 1, the ground state of the original model is a collinearly ordered antiferromagnet, which is separated from the incommensurate state by a quantum phase transition.
We use the example of the cuboctahedron, a highly frustrated molecule with 12 sites, to study the approach to the classical limit. We compute magnetic susceptibility, specific heat, and magnetic cooling rate at high magnetic fields and low temperatures for different spin quantum numbers s. Remarkably big deviations of these quantities from their classical counterparts are observed even for values of s which are usually considered to be almost classical.
In an extensive computational experiment, we test Polyakovs conjecture that under certain circumstances an isotropic Heisenberg model can develop algebraic spin correlations. We demonstrate the emergence of a multi-spin $text{U(1)}$ order parameter in a Heisenberg antiferromagnet on interpenetrating honeycomb and triangular lattices. The correlations of this relative phase angle are observed to decay algebraically at intermediate temperatures in an extended critical phase. Using finite-size scaling, we show that both phase transitions are of the Berezinskii-Kosterlitz-Thouless type and at lower temperatures, we find long-range $mathbb{Z}_6$ order.
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