Topological spin excitations of Heisenberg antiferromagnets in two dimensions

In this paper we discuss the construction and the dynamics of vortex-like topological spin excitations in the Schwinger-boson description of Heisenberg antiferromagnets in two dimensions. The topological spin excitations are Dirac fermions (with gap) when spin value S is a half-integer. Experimental and theoretical implications of these excitations are being investigated. 71.10.Fd,75.10.Jm,75.40.Gb Typeset using REVTEX 1 Recently there are strong interests in the study of Heisenberg antiferromagnets on two dimensional square lattice. Early theoretical analysis showed that the low energy, long length scale behaviour of the model should be described by the renormalized classical regime of the (2 + 1)d O(3) non-linear-sigma-model (NLσM) [1,2]. The analysis was believed to be valid as long as the length scale under investigation is much larger than lattice spacing. More recently, in a series of experiments [3] and Monte Carlo simulations [4–6], it was discovered that the length scale at which the renormalized classical σ-model description becomes valid is surprisingly long (L ≥ 200 sites for spin S = 1/2) [5,6]. Quantum Monte Carlo study of the low energy spectrum of the model on finite size lattices also suggested that the spectrum in the S = 1/2 case disagrees rather strongly with prediction of NLσM even when the size of the system N is not too small (N ≤ 32) [7]. These anomalous findings suggest that contrary to usual believe, there may exist an intermediate energy/length scale where the behaviours of the system deviates strongly from NLσM. On the other hand, it has been shown by Read and Chakraborty [8] that fermionic spin excitations exist as topological excitations in the short-ranged RVB phase of 2D S = 1/2 Heisenberg model, and their analysis has been generalized by the author [9] to the case (for arbitrary spin S) when the system is described by Schwinger-boson mean-field theory(SBMFT) [10]. These topological excitations are finite energy excitations of 2D Heisenberg antiferromagnets that do not appear in conventional NLσM description. However, the dynamics of the topological spin excitations were not investigated in those works [8,9]. The purpose of the present paper is to investigate, starting from SBMFT, the dynamics of the topological spin excitations constructed in Ref. [9] under some very general assumptions. In particular, we shall show that the existence of these topological excitations is consistent with the recently observed anomalous behaviours in the Heisenberg model. We shall also point out, in the case of S = 1/2 Heisenberg antiferromagnet, an interesting connection between the topological spin excitations and the spin excitations in the flux-phase [11] of fermionic RVB mean-field theory. To start with we review briefly the construction of topological spin excitations in SBMFT 2 of 2D Heisenberg model. Following Ref. [9] we assume that the low energy physics of general spin-S 2D Heisenberg model is described by the Schwinger-boson mean-field Hamiltonian