Turing-like patterns in an asymmetric dynamic Ising model.

To investigate novel aspects of pattern formation in spin systems, we use a mapping between reactive concentrations in a reaction-diffusion system and spin orientations in a dynamic multiple-spin Ising model. While pattern formation in Ising models always relies on infinite-range interactions, this mapping allows us to design a finite-range-interactions Ising model that can produce patterns observed in reaction-diffusion systems including Turing patterns with a tunable typical length scale. This model has asymmetric interactions and several spin types coexisting at a site. While we use the example of genetic regulation during embryogenesis to build our model, it can be used to study the behavior of other complex systems of interacting agents.

Chiral Spin Liquid on a Kagome Antiferromagnet Induced by the Dzyaloshinskii-Moriya Interaction.

The quantum spin liquid material herbertsmithite is described by an antiferromagnetic Heisenberg model on the kagome lattice with a non-negligible Dzyaloshinskii-Moriya interaction (DMI). A well-established phase transition to the q=0 long-range order occurs in this model when the DMI strength increases, but the precise nature of a small-DMI phase remains controversial. Here, we describe a new phase obtained from Schwinger-boson mean-field theory that is stable at small DMI, and which can explain the dispersionless spectrum seen in the inelastic neutron scattering experiment by Han et al. [Nature (London) 492, 406 (2012)NATUAS0028-083610.1038/nature11659]. It is a time-reversal symmetry breaking Z_{2} spin liquid, with the unique property of a small and constant spin gap in an extended region of the Brillouin zone. The phase diagram as a function of DMI and spin size is given, and dynamical spin structure factors are presented.

Entropy dependence of correlations in one-dimensional SU(N) antiferromagnets.

Motivated by the possibility to load multicolor fermionic atoms in optical lattices, we study the entropy dependence of the properties of the one-dimensional antiferromagnetic SU(N) Heisenberg model, the effective model of the SU(N) Hubbard model with one particle per site (filling 1/N) in the large U/t limit. Using continuous-time world-line Monte Carlo simulations for N=2-5, we show that characteristic short-range correlations develop at low temperature as a precursor of the ground state algebraic correlations. We also calculate the entropy as a function of temperature, and we show that the first sign of short-range order appears at an entropy per particle that increases with N and already reaches 0.8k(B) at N=4, in the range of experimentally accessible values.

Kagome antiferromagnet: a chiral topological spin liquid?

Inspired by the recent discovery of a new instability towards a chiral phase of the classical Heisenberg model on the kagome lattice, we propose a specific chiral spin liquid that reconciles different, well-established results concerning both the classical and quantum models. This proposal is analyzed in an extended mean-field Schwinger boson framework encompassing time reversal symmetry breaking phases, which allows both a classical and a quantum phase description. At low temperatures, we find that quantum fluctuations favor this chiral phase, which is stable against small perturbations of second- and third-neighbor interactions. For spin-1/2, this phase may be, beyond the mean field, a chiral gapped spin liquid. Such a phase is consistent with the density matrix renormalization group results of Yan et al. [Science 332, 1173 (2011)]. Mysterious features of the low-lying excitations of exact diagonalization spectra also find an explanation in this framework. Moreover, thermal fluctuations compete with quantum ones and induce a transition from this flux phase to a planar zero flux phase at a nonzero value of the renormalized temperature (T/S2), reconciling these results with those obtained for the classical system.