Topological Excitations in Quantum Spin Systems

Abstract

The origin and significance of topological excitations in quantum spin models in low dimensions are presented in detail. Besides a general review, our own work in this area is described in great depth. Apart from theoretical analysis of the existence and properties of spin vortices and antivortices, the possible experimental consequences and signatures are also highlighted. In particular, the distinguishing features between the even and odd charged topological excitations are brought out through a detailed analysis of the topological term in the quantum action. Moreover, an interesting symmetry property is predicted between the excitations from a ferromagnetic model and an antiferromagnetic model. Through a novel approach of ours, a bridge is established between field theoretical formalism and the well-known statistical mechanical treatment of Berezinskii-Kosterlitz-Thouless (BKT) transition involving these topological excitations. Furthermore, a detailed phenomenological analysis of the experimentally observed static and dynamic magnetic properties of the layered magnetic materials, possessing XY anisotropy in the in-plane spin-spin couplings, is undertaken to test the theoretical predictions regarding the behaviour of these excitations. The importance and the crucial role of quantum spin fluctuations in these studies are also brought out very clearly by our analysis.

The connection between vortex-like topological excitations and conventional excitations in quantum ferromagnetic spin systems on two-dimensional lattice and their stability

“…The validity of the BKT transition for this model has been confirmed [37,38]. A fullfledged quantum treatment has also been performed based on the application of path integral techniques using the coherent state basis, for XY-anisotropic Heisenberg ferromagnet on a square lattice [39,40]. The partition function for the above quantum spin model has been expressed in terms of an effective action containing a topological part (Wess-Zumino term) which contains a genuine topological term as a charge measuring object for the vortices/merons (anti-vortices/anti-merons) alongside a non-topological term.…”

“…We now start by defining a quantum spin vortex (anti-vortex) on a square lattice [36,39,40]. A charge 1 vortex (anti-vortex) is defined on a square plaquette as a spin configuration in which the spin direction (horizontal and vertical spins as defined below) rotates through an angle +2𝜋(−2𝜋) for a closed walk in an anti-clockwise (clockwise) direction around the plaquette.…”

“…It is worthwhile to mention that this situation corresponding to 𝜆 → 0 is very different from the case of 𝜆 = 0 corresponding to pure XY model. It is in this very limit that a vortex may be looked upon as a "flattened Meron" [39,40,60].…”

“…The question of existence of the topological excitations, namely, vortices and merons in twodimensional quantum ferromagnetic spin systems have been explored both numerically and analytically [36][37][38][39][40]. It has been determined numerically that in this case the vortex-anti-vortex pair density is nonzero even at T=0 [36].…”

“…The partition function for the above quantum spin model has been expressed in terms of an effective action containing a topological part (Wess-Zumino term) which contains a genuine topological term as a charge measuring object for the vortices/merons (anti-vortices/anti-merons) alongside a non-topological term. It has been shown that in the very large anisotropy limit (corresponding to 𝜆 → 0) the topological term can characterize the topological excitations viz., vortices and anti-vortices [39,40]. In this formalism, the topological term arises from the path integral formulation of the quantum partition function in contrast to the situation where the vorticity operator has been introduced heuristically [36].…”