Interplay of Spin and Spatial Anisotropy in Low-Dimensional Quantum Magnets with Spin 1/2

Abstract

Quantum Heisenberg chain and square lattices are important paradigms of a low-dimensional magnetism. Their ground states are determined by the strength of quantum fluctuations. Correspondingly, the ground state of a rectangular lattice interpolates between the spin liquid and the ordered collinear Néel state with the partially reduced order parameter. The diversity of additional exchange interactions offers variety of quantum models derived from the aforementioned paradigms. Besides the spatial anisotropy of the exchange coupling, controlling the lattice dimensionality and ground-state properties, the spin anisotropy (intrinsic or induced by the magnetic field) represents another important effect disturbing a rotational symmetry of the spin system. The S = 1/2 easy-axis and easy-plane XXZ models on the square lattice even for extremely weak spin anisotropies undergo Heisenberg-Ising and Heisenberg-XY crossovers, respectively, acting as precursors to the onset of the finite-temperature phase transitions within the two-dimensional Ising universality class (for the easy axis anisotropy) and a topological Berezinskii-Kosterlitz-Thouless phase transition (for the easy-plane anisotropy). Experimental realizations of the S = 1/2 two-dimensional XXZ models in bulk quantum magnets appeared only recently. Partial solutions of the problems associated with their experimental identifications are discussed and some possibilities of future investigations in quantum magnets on the square and rectangular lattice are outlined.Heisenberg models [6][7][8]. Berezinskii revealed that eigenstates of the Hamiltonian describing the 2D lattice of planar rotators, 2D Bose liquid, and 2D XY magnet can be sorted into two classes; localized "vortices" characterized by a nonzero circulation along a minimum closed contour of the square lattice and displaced harmonic oscillations-spin waves with zero circulation [9,10]. Below a critical temperature related to some phase transition, the vortices form configurations with a total zero circulation. Kosterlitz and Thouless introduced a definition of a topological long-range order adopted from the dislocation theory of melting [11]. In a 2D crystal, authors showed that at low temperatures, dislocations with Burgers vector of the magnitude b tend to form closely bound dipole pairs with resulting b = 0. Above some critical temperature, the pairs start to dissociate and the dislocations will appear spontaneously. The same type of argument can be applied for the 2D XY model and 2D neutral superfluid. While in the 2D XY model, a logarithmically large energy barrier, V(r)~-ln(r), stabilizes a topological order formed by the bound pairs of vortices, in the case of the 2D Heisenberg model, there is no topological order, since energy barriers separating different configurations are small, allowing continuous changes between individual configurations [11].Many theoretical studies showed that phase transitions in the 2D systems such as granular superconducting films, superfluid films, 2D Coulomb gas etc., with c...

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