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Register a new userLarge off diagonal exchange couplings and spin liquid states in $mathbf{C_3}$ symmetric iridates
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Iridate oxides on a honeycomb lattice are considered promising candidates for realization of quantum spin liquid states. We investigate the magnetic couplings in a structural model for a honeycomb iridate K$_2$IrO$_3$, with $C_3$ point group symmetry at the Ir sites, which is an end member of the recently synthesized iridate family K$_x$Ir$_y$O$_2$. Using textit{ab-initio} quantum chemical methods, we elucidate the subtle relationship between the real space symmetry and magnetic anisotropy and show that the higher point group symmetry leads to high frustration with strong magnetic anisotropy driven by the unusually large off-diagonal exchange couplings ($Gamma$s) as opposed to other spin-liquid candidates considered so far. Consequently, large quantum fluctuations imply lack of magnetic ordering consistent with the experiments. Exact diagonalization calculations for the fully anisotropic $K$-$J$-$Gamma$ Hamiltonian reveal the importance of the off-diagonal anisotropic exchange couplings in stabilizing a spin liquid state and highlight an alternative route to stabilize spin liquid states for ferromagnetic $K$.
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We report a new classical spin liquid in which the collective flux degrees of freedom break the translation symmetry of the honeycomb lattice. This exotic phase exists in frustrated spin-orbit magnets where a dominant off-diagonal exchange, the so-called $Gamma$ term, results in a macroscopic ground-state degeneracy at the classical level. We demonstrate that the system undergoes a phase transition driven by thermal order-by-disorder at a critical temperature $T_c approx 0.04 |Gamma|$. At first sight, this transition reduces an emergent spherical spin-symmetry to a cubic one: spins point predominantly toward the cubic axes at $T < T_c$. However, this seems to simply restore the cubic symmetry of the $Gamma$ model, and the non-coplanar spins remain disordered below $T_c$. We show that the phase transition actually corresponds to plaquette ordering of hexagonal fluxes and the cubic symmetry is indeed broken, a scenario that is further confirmed by our extensive Monte Carlo simulations.
We show that the off-diagonal exchange anisotropy drives Mott insulators with strong spin-orbit coupling to a classical spin liquid regime, characterized by an infinite number of ground states and Ising variables living on closed or open strings. Depending on the sign of the anisotropy, quantum fluctuations either fail to lift the degeneracy down to very low temperatures, or select non-collinear magnetic states with unconventional spin correlations. The results apply to all 2D and 3D tri-coordinated materials with bond-directional anisotropy, and provide a consistent interpretation of the suppression of the x-ray magnetic circular dichroism signal reported recently for $beta$-Li$_2$IrO$_3$ under pressure.
We present a large-scale density matrix renormalization group (DMRG) study of the spin-$1$ SU(3) bilinear-biquadratic model on the square lattice, which was shown to host a nematic spin liquid state in recent DMRG calculations. We report that this spin liquid appears to strongly compete with a three-sublattice magnetic order. To further study the competition between the two states, and the reason of the emergent nematic spin liquid, we included an additional next-nearest-neighbor SU(3) symmetric interactions along one of the two plaquette diagonal directions. This allows to tune the square-lattice model to the triangular-lattice model. By computing spin correlation functions and various order parameters, we find that the three-sublattice order may develop at infinitesimal additional new coupling, at least within the precision of our study. Compared with the previous findings that the nematic spin liquid is stable in extended parameter regions with additional couplings that respect the lattice symmetries of the square lattice, we argue that here the diagonal couplings, which frustrate the bipartite-lattice structure, rapidly suppress the two-sublattice fluctuations and the three-sublattice order thus wins. This numerical result is consistent with the conjecture that the nematic spin liquid emerges from the competition between two- and three-sublattice fluctuations.
We present a model for conductivity and energy diffusion in a linear chain described by a quadratic Hamiltonian with Gaussian noise. We show that when the correlation matrix is diagonal, the noise-averaged Liouville-von Neumann equation governing the time-evolution of the system reduces to the Lindblad equation with Hermitian Lindblad operators. We show that the noise-averaged density matrix for the system expectation values of the energy density and the number density satisfy discre
This article is an introductory review of the physics of quantum spin liquid (QSL) states. Quantum magnetism is a rapidly evolving field, and recent developments reveal that the ground states and low-energy physics of frustrated spin systems may develop many exotic behaviors once we leave the regime of semi-classical approaches. The purpose of this article is to introduce these developments. The article begins by explaining how semi-classical approaches fail once quantum mechanics become important and then describes the alternative approaches for addressing the problem. We discuss mainly spin $1/2$ systems, and we spend most of our time in this article on one particular set of plausible spin liquid states in which spins are represented by fermions. These states are spin-singlet states and may be viewed as an extension of Fermi liquid states to Mott insulators, and they are usually classified in the category of so-called $SU(2)$, $U(1)$ or $Z_2$ spin liquid states. We review the basic theory regarding these states and the extensions of these states to include the effect of spin-orbit coupling and to higher spin ($S>1/2$) systems. Two other important approaches with strong influences on the understanding of spin liquid states are also introduced: (i) matrix product states and projected entangled pair states and (ii) the Kitaev honeycomb model. Experimental progress concerning spin liquid states in realistic materials, including anisotropic triangular lattice systems ($kappa$-(ET)$_{2}$Cu$_{2}$(CN)$_{3}$ and EtMe$_{3}$Sb[(Pd(dmit)$_{2}$]$_{2}$), kagome lattice systems (ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$) and hyperkagome lattice systems (Na$_{4}$Ir$_{3}$O$_{8}$), is reviewed and compared against the corresponding theories.
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