Quantum Spin Liquid Phase in the Shastry–Sutherland Model Detected by an Improved Level Spectroscopic Method
Ling Wang1*, Yalei Zhang2, and Anders W. Sandvik3,4*
1Department of Physics, Zhejiang University, Hangzhou 310000, China 2Beijing Computational Science Research Center, Beijing 100193, China 3Department of Physics, Boston University, Boston, Massachusetts 02215, USA 4Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
Abstract：We study the spin-$1/2$ two-dimensional Shastry–Sutherland spin model by exact diagonalization of clusters with periodic boundary conditions, developing an improved level spectroscopic technique using energy gaps between states with different quantum numbers. The crossing points of some of the relative (composite) gaps have much weaker finite-size drifts than the normally used gaps defined only with respect to the ground state, thus allowing precise determination of quantum critical points even with small clusters. Our results support the picture of a spin liquid phase intervening between the well-known plaquette-singlet and antiferromagnetic ground states, with phase boundaries in almost perfect agreement with a recent density matrix renormalization group study, where much larger cylindrical lattices were used [J. Yang et al., Phys. Rev. B 105, L060409 (2022)]. The method of using composite low-energy gaps to reduce scaling corrections has potentially broad applications in numerical studies of quantum critical phenomena.
. [J]. 中国物理快报, 2022, 39(7): 77502-077502.
Ling Wang, Yalei Zhang, and Anders W. Sandvik. Quantum Spin Liquid Phase in the Shastry–Sutherland Model Detected by an Improved Level Spectroscopic Method. Chin. Phys. Lett., 2022, 39(7): 77502-077502.
Though these triplets with energy between $E(T_{1})$ and $E(T_{2})$ have lattice quantum numbers different from those of $T_{1}$ and $T_{2}$, the corresponding symmetries are not implemented in the DMRG calculation (but the total spin symmetry is implemented in this case), only computed as expectation values with the states obtained. The states have to be generated one-by-one starting from the lowest one and convergence of this procedure becomes increasingly challenging with the number of states computed (Refs.[31, 33]) and we have not been able to reach the state with quantum numbers corresponding to $T_{2}$ for $N=40$.
2022, Vol. 39 
