Abstract:

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.

Key words: tensor renormalization group methods, frustrated quantum magnets, microscopic spin models, quantum spin liquid states