Analysis On The Finite-temperature Phase Transition Of Heisenberg Antiferroniagnetic Compound LIVGe₂O₆

The analysis on one-dimensional integer-spin Heisenberg antiferromagnets has attracted much attention since Haldane predicted that for integer spin chain there exists an energy gap between the ground state and the lowest-excited state but the half-odd-integer chain is gapless due to the existence of the topology term in1983. Experimentally the Haldane gap materials have been observed, and LiVGe2O6is one of them. The susceptibility and nuclear magnetic resonance measurements on LiVGe2O6indicate that this material shows a phase transition from paramagnetic state to antiferromagnetic Neel state at about22K, and there exists a gap between the ground state and triplet excited states in the low-temperature magnetic excitation spectrum. Based on the model Hamiltonian of LiVGe2O6, we introduce a low-energy field theory-Ginzburg-Landau theory to describe the magnetic properties of this compound. Then from this theory, we study the finite-temperature phase transition of LiVGe2O6due to spontaneous symmetry breaking and the temperature dependence of magnetic susceptibility in low temperature region. We perform the numerical calculations with Mathematica, and all the theoretical results fit the experimental data very well. Our calculations also show that the phase transition at about22K is a first-order transition induced by the quantum fluctuations.