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...

We present a new method for a systematic spin-wave expansion for the quantum fluctuations of a generic spin Hamiltonian in a finite lattice, where the inverse spin magnitude 1/S is a well-defined expansion parameter. The first two leading contributions of the spin-spin correlation function are evaluated for the J1-J2 Heisenberg model. Very good agreement between our finite-size predictions and the exact diagonalization and Monte Carlo results is found for J2/J1 < 0.2 and S = 1/2, thus confirming the existence of antiferromagnetic long-range order in this J region. For J2/J1 > 0.3 the expansion is poorly converging, suggesting a possible breakdown of the spin-wave approximation. Here our calculation seems consistent with a possible spin liquid ground state.

The one-hole spectral weight for two chains and two dimensional lattices is studied numerically using a new method of analysis of the spectral function within the Lanczos iteration scheme: the Lanczos spectra decoding method.This technique is applied to the t−J z model for J z → 0, directly in the infinite size lattice. By a careful investigation of the first 13 Lanczos steps and the first 26 ones for the two dimensional and the two chain cases respectively, we get several new features of the one-hole spectral weight. A sharp incoherent peak with a clear momentum dispersion is identified, together with a second broad peak at higher energy. The spectral weight is finite up to the Nagaoka energy where it vanishes in a non-analytic way. Thus the lowest energy of one hole in a quantum antiferromagnet is degenerate with the Nagaoka energy in the thermodynamic limit. 75.10.Jm,75.40.Mg,71.10.+x Typeset using REVT E X 1

We review in details a recently proposed technique to extract information about dynamical correlation functions of many-body hamiltonians with a few Lanczos iterations and without the limitation of finite size. We apply this technique to understand the low energy properties and the dynamical spectral weight of a simple model describing the motion of a single hole in a quantum antiferromagnet: the t − J z model in two spatial dimension and for a double chain lattice. The simplicity of the model allows us a well controlled numerical solution, especially for the two chain case. Contrary to previous approximations we have found that the single hole ground state in the infinite system is continuously connected with the Nagaoka fully polarized state for J z → 0. Analogously we have obtained an accurate determination of the dynamical spectral weight relevant for photoemission experiments. For J z = 0 an argument is given that the spectral weight vanishes at the Nagaoka energy faster than any power law, as supported also by a clear numerical evidence. It is also shown that spin charge decoupling is an exact property for a single hole in the Bethe lattice but does not apply to the more realistic lattices where the hole can describe closed loop paths.

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