The exotic spin states and quantum effects in frustrated magnets have attracted
intensive research interest in recent years, which also have intimate connections with hightemperature
superconductivity and topological quantum computing, etc. Experimentally, people
have focused on typical spin liquid candidate materials including the triangular-, kagomeand
Kitaev honeycomb-lattice frustrated magnets. However, it constitutes a very challenging
many-body problem to clarify the quantum states and phase transitions therein. Recently, we
point out that it is possible to establish a protocol for understanding and explaining experiments
of frustrated magnets in an unbiased manner. By employing the finite-temperature tensor
renormalization group methods, we carry out accurate calculations and analyses of thermodynamic
properties, determine the microscopic spin model of the frustrated magnets, and
make further theoretical predictions. Below, we firstly introduce the recently proposed tensor
renormalization group (TRG) methods, including the linear and exponential TRG, and discuss
their applications on the triangular-lattice quantum Ising magnet TmMgGaO4 and the Kitaevhoneycomb
material α-RuCl3. We demonstrate that the finite-temperature TRG approaches
shed light on the study of spin liquid candidate materials, and could facilitate cutting-edge
research in the field of strongly correlated quantum systems.
