Quantum Hamiltonian formalism and symmetry crossover in one dimension for weakly anisotropic Heisenberg and planar systems

Abstract

A quantum Hamiltonian formalism is developed for weakly anisotropic Heisenberg (O(3)) and planar (O(2)) ferromagnetic classical spin systems in one dimension. This formalism is then used to derive explicit formulas for the Heisenberg-Ising, Heisenberg-XY, and XY-Ising crossovers at low temperatures. This approach gives the correct thermodynamic properties both above and below the crossover temperature, when this temperature is much less than the mean-field critical temperature.