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

Abstract

Based on exact diagonalization and density matrix renormalization group method, we show that an anisotropic triangular lattice Heisenberg spin model has three distinct quantum phases. In particular, a spin-liquid phase is present in the weak interchain coupling regime, which is characterized by an anisotropic spin structure factor with an exponential-decay spin correlator along the weaker coupling direction, consistent with the Cs 2 CuCl 4 compounds. 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.14 The Heisenberg models on the square lattice with thirdnearest-neighbor couplings may also have a spin-liquid ground state as revealed by recent numerical studies based on density matrix renormalization group ͑DMRG͒ calculations. 15From the experimental point of view, the HAFM on an anisotropic triangular lattice is particularly interesting as it is directly relevant to the quantum magnet in the Cs 2 CuCl 4 compounds, 16-18 which may be described by a minimal model at half-filling ͑Ref. 19͒:Here S i are spin-1 / 2 operators, and J, JЈ ജ 0 are the nearestneighbor couplings along the chain ͑J͒ and the other two axes ͑JЈ͒ between different chains on a triangular lattice. Based on the variational Monte Carlo ͑VMC͒ method, a resonating valence bond ͑RVB͒ wave function was previously proposed 19 to describe the low-lying anisotropic spin excitation observed experimentally [16][17][18] in these systems, which suggests a gapless spin-liquid state. The model has also been studied by different analytic approaches such as spin wave theory ͑SWT͒, 6 large-S expansion, 8 as well as the series expansion. 20,21 These works have predicted magnetic ordered states at JЈ ജ 0.3J ± 0.03J side, while the magnetic order vanishes on the smaller JЈ side suggesting a disordered phase. The recent series expansion study by Zheng et al. 21 has further indicated that quantum renormalizations strongly enhance the one dimensionality of the spectra, which implies that a more accurate description of quantum effects is needed. Thus exact calculations with taking into account all the quantum fluctuations are highly desirable in order to further establish of exi...

Ground states of spin-12triangular antiferromagnets in a magnetic field

“…At zero field, there is already considerable work on the spatially anisotropic Heisenberg model in two dimensions 10,[40][41][42][43][44][45] . Away from the quasi-1d region, i.e.…”

Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice

“…Theoretically, QSLs have been sought in spin-1/2 antiferromagnets with frustrated and/or competing interactions on triangular [28][29][30][31] , honeycomb [32][33][34][35][36] , square [37][38][39] , and kagomé [40][41][42][43][44] lattices. Amongst all these, the kagomé Heisenberg model (KHM) appears to possess the most robust QSL phase, and the only one consistently found in unbiased density matrix renormalization group (DMRG) calculations.…”

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.…”