Realization of a spin liquid in a two dimensional quantum antiferromagnet

Abstract

The ground state properties of the two dimensional spatially anisotropic Heisenberg model are investigated by use of field theory mappings, spin-wave expansion, and Lanczos technique. Evidence for a disorder transition induced by anisotropy at about Jy/Jx < 0.1 is shown. We argue that the disordered phase is gapless and its long wavelength properties can be interpreted in terms of decoupled one dimensional chains.PACS numbers: 75.10.Jm, 75.30.Ds The search for disordered (spin liquid) ground states in two dimensional (2D) electronic models has been pursued since the seminal work of Fazekas and Anderson [1] on quantum antiferromagnets (QAF) in frustrating lattices. This problem has been revived in the last few years due to the resonating valence bond conjecture [2], which stimulated much numerical work on the subject. Despite considerable effort, the existing evidence in favor of a spin liquid in 2D frustrated QAF is weak at best [3,4], with the single exception of the kagome QAF where a disordered ground state is plausible [5], even if the presence of nonconventional magnetic order is still a possibility.In this Letter, we present analytical as well as numerical evidence supporting an order-disorder transition in the square lattice 5 = 1/2 QAF driven by spatial anisotropy in the nearest neighbor coupling. This model does not introduce frustration and therefore presents several advantages with respect to the previously investigated systems, the most important being the absence of any plausible order parameter competing with the Neel staggered magnetization m = ^j^ SR exp(Q • R) [Q = ('7r,7r)]. The model is defined by the Hamiltonian Rwhere SR are spin 1/2 operators living on a square lattice, X and y are unit vectors, J > 0, and a < 1. The isotropic limit (a = 1) has been extensively studied by exact diagonalizations [6] and quantum Monte Carlo [7,8] with the resulting evidence of a finite staggered magnetization in the thermodynamic limit [8] m ~ 0,3075, quite close to the spin-wave theory (SWT) estimate m = 0.3034 [9]. Physically, the strongly anisotropic model (1) describes a system of weakly coupled AF chains whose study has attracted considerable interest among theoreticians and experimentalists in view of the possibility to observe the peculiar features of one dimensional physics [10].The presence of an order-disorder transition in model (1) has been conjectured by several authors [11,12] and can be motivated by the standard mapping of the 2D quantum model (1) into the (2+1) dimensional 0(3) nonlinear sigma model (NLaM) defined by the action S=^Jdxdydt[T,(a,n)2 + Tyidyiif + Xo{dtn)^] ,(2) where n is a unit vector. The lowest order estimates of the parameters give Tx = J'/4, Ty = a J/4, Xo^ -4a^ J(l + a) where a is the lattice spacing. Two limits of the action (2) can be easily analyzed: The isotropic model is known to be ordered for the physically relevant parameters [13], while the a -^ 0 limit of the action (2) correctly describes a stack of uncoupled (1+1) dimensional models which are disordered a...

Reduction of Ordered Moment and Néel Temperature of Quasi-One-Dimensional AntiferromagnetsSr2CuO3andKojima1, Fudamoto2, Larkin3 et al. 1997Phys. Rev. Lett.187201441View full textAdd to dashboardCite

“…Previously, it was proposed that there is a non-zero critical coupling ratio (J ′ /J = R c ), below which the system retains a singlet ground-state [5]. Recent renormalization group calculations however suggest that the ground state may depend on microscopic details of the model which describes the spin-spin interactions [6,7].…”

Resonating Valence Bond Theory of Coupled Heisenberg Chains

“…It has been proposed that the system can be described in terms of a short-range resonating valence bond (RVB) picture [6,8], and mean field treatments with Gutzwiller renormalization of the matrix elements have supported this conclusion. It has also been suggested that in contrast, systems with an odd number of chains n c are gapless [7,8].…”

“…A number of studies [3][4][5][6][7][8] have provided strong evidence that at half-filling the two-chain ladder systems are spin liquids, with a spin-gap and finite spin-spin correlation length. It has been proposed that the system can be described in terms of a short-range resonating valence bond (RVB) picture [6,8], and mean field treatments with Gutzwiller renormalization of the matrix elements have supported this conclusion.…”

Spin-wave analysis to the spatially anisotropic Heisenberg antiferromagnet on a triangular lattice

“…This should be compared with the spin wave value for the square case 16 , J ⊥ /J ∼ 0.03, where the difference in one order of magnitude shows that the way in which fluctuations overcome the ordering is different. However, in the regime around η = 1 the spin wave calculation is not reliable any more since quantum fluctuations are divergent in the 1D limit.…”