Low-temperature properties of two-dimensional frustrated quantum antiferromagnets

Abstract

Though much of the recent work on 2D quantum canted antiferromagnets has been devoted to the study of disordered states, there is evidence that some of these systems have Neel ground states, even for spin y. Following Chakravarty, Halperin, and Nelson, we study the quantum nonlinear sigma model suited to these systems and obtain for the correlation length ^'=C^lA/(kBT)^^^e " * , where A and B depend on the spin stiffnesses and spin-wave velocities renormalized by quantum fluctuations. We discuss experiments on ^He adsorbed on Grafoil.PACS numbers: 75.10.Jm, 74.65.+n, 75.50.Ee Since at the classical level the effect of frustration is to reduce the order, frustrated quantum spin systems are expected to exhibit nonconventional disordered ground states [l]. Such an effect would be of importance for some theories of high-r^ superconductivity [2,3]. For this reason, quantum frustrated spin models have recently been the object of intensive numerical as well as analytical work [4][5][6][7][8]. Though most of the theoretical interest has been devoted to the study of states not having longrange order, it is likely that some frustrated models may exhibit long-range order in their ground states [6-8], even for spin y. To our knowledge, there have been no studies of the low-temperature properties of frustrated quantum antiferromagnets assuming a noncollinear ordered ground state (which will be referred to as a Neel state in the following). In particular, the expression for the correlation length for these systems is still lacking. Such an expression would be of interest in discussing experiments on doped La2Cu04 [9,10] and on ^He [11] adsorbed on a graphite substrate. In this work, we extend the analysis of Chakravarty, Halperin, and Nelson (CHN) [12,13] to quantum canted Heisenberg models with zero net magnetization. We study the quantum nonlinear sigma (QNLa) model suited to these systems and give the general expression of their correlation length.Years ago, Halperin and Saslow [14] showed that the long-distance physics of frustrated quantum Heisenberg models may be described by a hydrodynamical theory, provided the total magnetization is zero. They predicted the existence of three spin-wave excitations resulting from the complete breaking of the 0(3) spin-rotation group. The linear spectrum and the interactions of these spin-wave excitations are described by a QNLa model whose action is entirely determined by symmetries. This action was first derived from the lattice by Dombre and Read [15] in the special case of the D = 2 triangular Heisenberg antiferromagnet (AFT). They wrote it in terms of a rotation matrix of SO(3) which is the relevant order parameter for such a model:where g(x,r) € SO(3), 9^, = (9o,8/) =(9/9r,d/ax/), / = 1,2, p is the inverse temperature, and /^^ =diag(/7ip, P2ft.P}fi\ iU=0,±, are diagonal matrices which are a priori independent. It is important to notice that action (l) is not particular to the AFT model. In fact, if not for the anisotropy between space and time directions, action (1) would be th...

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