Large-Nsolutions of the Heisenberg and Hubbard-Heisenberg models on the anisotropic triangular lattice: application to Cs₂CuCl₄and to the layered organic superconductors κ-(BEDT-TTF)₂X (BEDT-TTF≡bis(ethylene-dithio)tetrathiafulvalene); X≡anion)

Abstract

We solve the Sp(N) Heisenberg and SU(N) Hubbard-Heisenberg models on the anisotropic triangular lattice in the large-N limit. These two models may describe respectively the magnetic and electronic properties of the family of layered organic materials κ-(BEDT-TTF)2X. The Heisenberg model is also relevant to the frustrated antiferromagnet, Cs2CuCl4. We find rich phase diagrams for each model. The Sp(N) antiferromagnet is shown to have five different phases as a function of the size of the spin and the degree of anisotropy of the triangular lattice. The effects of fluctuations at finite-N are also discussed. For parameters relevant to Cs2CuCl4 the ground state either exhibits incommensurate spin order, or is in a quantum disordered phase with deconfined spin-1/2 excitations and topological order. The SU(N) Hubbard-Heisenberg model exhibits an insulating dimer phase, an insulating box phase, a semi-metallic staggered flux phase (SFP), and a metallic uniform phase. The uniform and SFP phases exhibit a pseudogap. A metal-insulator transition occurs at intermediate values of the interaction strength.

Planar pyrochlore antiferromagnet: A large-Nanalysis

“…Indeed geometrically frustrated magnets seem to allow multifarious quantum-disordered paramagnetic phases, including various translational-symmetry-breaking phases 8 and the quantum spin liquid phases with fractionalized excitations. 8,9,10,11 It has been suggested that some of these quantum-disordered phases may also arise in underdoped cuprate superconductors, where the frustration of the spins may occur due to the motion of doped holes.…”

Spin-liquid phase due to competing classical orders in the semiclassical theory of the Heisenberg model with ring exchange on an anisotropic triangular lattice

“…However, later numerical work [52] has shown that the ground state has "120 • order"-a special case of spiral order, discussed below, with an ordering wave vector Q = (2π/3,2π/3). A range of other methods have been used to study the Heisenberg model on the anisotropic triangular lattice including linear spin-wave theory [53,54], modified spin-wave theory [55], series expansions [12,56], the coupled cluster method [57], large-N expansions [58], variational Monte Carlo [59], resonating valence bond theory [15,19,[60][61][62], pseudofermion functional renormalization group [63], slave rotor theory [64], renormalization group [65], and the density matrix renormalization group [66]. These calculations show that for small J /J , Néel (π,π) order is realised and spiral (q,q) long-range AFM order is realized for J /J ∼ 1.…”

Spin-liquid phase in an anisotropic triangular-lattice Heisenberg model: Exact diagonalization and density-matrix renormalization group calculations

“…In the obtained phase diagram, the spin-liquid phase is found to persist up to a relatively large critical anisotropic coupling ratio JЈ / J = 0.78, which is stabilized by strong quantum fluctuations, with a parity symmetry distinct from two magnetic ordered states in the stronger coupling regime. Two-dimensional ͑2D͒ frustrated spin systems have attracted intensive studies as they may exhibit unconventional magnetic properties.1-4 The isotropic spin-1 / 2 Heisenberg antiferromagnet ͑HAFM͒ on a triangular lattice was a candidate for the realization of a disordered spin-liquid phase, 1 but it turns out to exhibit a three-sublattice antiferromagneticlong-range-order ͑AFLRO͒ as established by analytic [5][6][7][8] and numerical 5,9,10 studies. Among various spin models, a spin-liquid phase has been established for more geometrically frustrated systems on the Kagome lattice, 11,12 dimer models, 13 and models involving four spin exchange terms.…”

“…1-4 The isotropic spin-1 / 2 Heisenberg antiferromagnet ͑HAFM͒ on a triangular lattice was a candidate for the realization of a disordered spin-liquid phase, 1 but it turns out to exhibit a three-sublattice antiferromagneticlong-range-order ͑AFLRO͒ as established by analytic [5][6][7][8] and numerical 5,9,10 studies. Among various spin models, a spin-liquid phase has been established for more geometrically frustrated systems on the Kagome lattice, 11,12 dimer models, 13 and models involving four spin exchange terms.…”