Phase Diagram of the J1, J2, J3 Heisenberg Models on the Honeycomb Lattice: A Series Expansion Study

We study magnetically ordered phases and their phase boundaries in the $J_1-J_2-J_3$ Heisenberg models on the honeycomb lattice using series expansions around N\'eel and different colinear and non-colinear magnetic states. An Ising anisotropy ($\lambda=J_{\perp}/J_z\ne 1$) is introduced and ground state energy and magnetization order parameter are calculated as a power seies expansion in $\lambda$. Series extrapolation methods are used to study properties for the Heisenberg model ($\lambda=1$). We find that at large $J_3$ ($>0.6$) there is a first order transition between N\'eel and columnar states, in agreement with the classical answer. For $J_3=0$, we find that the N\'eel phase extends beyond the region of classical stability. We also find that spiral phases are stabilized over large parameter regions, although their spiral angles can be substantially renormalized with respect to the classical values. Our study also shows a magnetically disordered region at intermedaite $J_2/J_1$ and $J_3/J_1$ values.Comment: 6 pages, 9 figure

Ground state properties, excitation spectra and phase transitions in the S=1/2S=1/2 and S=3/2S=3/2 bilayer Heisenberg models on the honeycomb Lattice

Motivated by the observation of a disordered spin ground state in the $S=3/2$ material Bi$_3$Mn$_4$O$_{12}$NO$_3$, we study the ground state properties and excitation spectra of the $S=3/2$ (and for comparison $S=1/2$) bilayer Heisenberg model on the honeycomb lattice, with and without frustrating further neighbor interactions. We use series expansions around the N\'eel state to calculate properties of the magnetically ordered phase. Furthermore, series expansions in $1/\lambda=J_1/J_{\perp}$, where $J_1$ is an in-plane exchange constant and $J_\perp$ is the exchange constant between the layers are used to study properties of the spin singlet phase. For the unfrustrated case, our results for the phase transitions are in very good agreement with recent Quantum Monte Carlo studies. We also obtain the excitation spectra in the disordered phase and study the change in the critical $\lambda$ when frustrating exchange interactions are added to the $S=3/2$ system and find a rapid suppression of the ordered phase with frustration. Implications for the material Bi$_3$Mn$_4$O$_{12}$NO$_3$ are discussed.Comment: 5 pages, 6 figure

Discerning Incompressible and Compressible Phases of Cold Atoms in Optical Lattices

Experiments with cold atoms trapped in optical lattices offer the potential to realize a variety of novel phases but suffer from severe spatial inhomogeneity that can obscure signatures of new phases of matter and phase boundaries. We use a high temperature series expansion to show that compressibility in the core of a trapped Fermi-Hubbard system is related to measurements of changes in double occupancy. This core compressibility filters out edge effects, offering a direct probe of compressibility independent of inhomogeneity. A comparison with experiments is made

Universal Finite Temperature Properties of a Three Dimensional Quantum Antiferromagnet in the Vicinity of a Quantum Critical Point

We consider a 3-dimensional quantum antiferromagnet which can be driven through a quantum critical point (QCP) by varying a tuning parameter g. Starting from the magnetically ordered phase, the N{\'e}el temperature will decrease to zero as the QCP is approached. From a generic quantum field theory, together with numerical results from a specific microscopic Heisenberg spin model, we demonstrate the existence of universal behaviour near the QCP. We compare our results with available data for TlCuCl_

Spin-waves in the J1a−J1b−J2J_{1a}-J_{1b}-J_{2} orthorombic square-lattice Heisenberg models: Application to the iron pnictide materials

Motivated by the observation of spatially anisotropic exchange constants in the iron pnictide materials, we study the spin-wave spectra of the $J_{1a}-J_{1b}-J_{2}$ Heisenberg models on a square-lattice with nearest neighbor exchange $J_{1a}$ along x and $J_{1b}$ along y axis and a second neighbor exchange $J_2$. We focus on the regime, where the spins order at ($\pi,0$), and compute the spectra by systematic expansions around the Ising limit. We study both spin-half and spin-one Heisenberg models as well as a range of parameters to cover various cases proposed for the iron pnictide materials. The low-energy spectra have anisotropic spin-wave velocities and are renormalized with respect to linear spin-wave theory by up to 20 percent, depending on parameters. Extreme anisotropy, consisting of a ferromagnetic $J_{1b}=- |J_F|$, is best distinguished from a weak anisotropy ($J_{1a}\approx J_{1b}=J_1$, $J_2>J_1/2$) by the nature of the spin-waves near the wavevectors ($0,\pi$) or ($\pi,\pi$). The reported spectra for the pnictide material CaFe$_2$As$_2$ clearly imply such an extreme anisotropy.Comment: 6 pages, 10 figure

Thermodynamics of strongly interacting fermions in two-dimensional optical lattices

We study finite-temperature properties of strongly correlated fermions in two-dimensional optical lattices by means of numerical linked cluster expansions, a computational technique that allows one to obtain exact results in the thermodynamic limit. We focus our analysis on the strongly interacting regime, where the on-site repulsion is of the order of or greater than the band width. We compute the equation of state, double occupancy, entropy, uniform susceptibility, and spin correlations for temperatures that are similar to or below the ones achieved in current optical lattice experiments. We provide a quantitative analysis of adiabatic cooling of trapped fermions in two dimensions, by means of both flattening the trapping potential and increasing the interaction strength.Comment: 7 pages, 7 figure