Low-dimensional magnetic materials have attracted much attention due to their exotic ground states, rich physical properties, and their close relationship to high superconductor materials. Studies on the physical properties of the low-dimensional magnetic materials are useful to probe the mechanism of the fantastic phenomena and develop new function materials. This dissertation focuses on the quantum phase transition induced by magnetic field and role of magnetic excitations in the heat transport of low-dimensional magnetic materials. The low-temperature heat transport properties of the spin-dimer material with BEC transition, the one-dimensional magnetic material and the organic spin chain material with staggered magnetization are studied. Low-dimensional magnetic materials provides research related to the quantum ground state and the excited state model, the new phase and the unique possibility of competition between quantum fluctuations and thermal fluctuations, so for quasi-one-dimensional magnetic materials research has developed into an independent research. From a theoretical point of view, this research provides a broad platform for a variety of theoretical and computational methods.