Magnetization Of The Spin-1/2 Heisenberg Antiferromagnet On The Triangular Lattice

In low-dimensional frustrated systems,the spin-1/2(h=1)Heisenberg antiferromagnet on the triangular lattice is quite important.Anderson proposed the quantum spin liquid state based on the study of this model firstly.The exotic state surmounts Landau's symmetry-broken paradigm and has fractional excitation,which has the attention of scientists.Moreover,the triangular lattice intuitively shows the characteristics of the system's frustration,which provides a perfect commence for learning frustration and quantum fluctuation in quantum many-body systems.After decades of debate,now there is a rough consensus that at zero temperature the spin-1/2 Heisenberg antiferromagnet on the triangular lattice is three-sublattice 120° magnetically ordered,in contrast to a quantum spin liquid as originally proposed.However,there remains a considerable discrepancy in the magnetization reported among various methods.To resolve this issue,in this work we revisit this model by the tensor-network state algorithm.The main content of this paper is divided into two parts:the first part is to calculate the ground-state properties by the tensor-network state algorithm with projected entangled simplex state(PESS)ansatz.The PESS ansatz can capture the three-body correlation in this model,and the maximum bond dimension D is 13 in the calculation.The results show that Eb=-0.18334(10)(J=1)is consistent with consequences from DMRG and GFMC.The magnetization M=0.161(5)is slightly smaller than 1/3 of its classical value.In particular,it is smaller than all that obtained in previous works(see Table 3-1),which means we provide a new magnetization benchmark.We also calculate the angles between all the nearest neighbors in the unit cell and the many-body correlation in this model.The 1200 angles between nearest neighbors are almost perfect.The tripartite correlation becomes more and more significant as D increases.These results make us more confident that the ground state is ordered.In the second part,we recalculated the model using linear spin wave theory,obtained the ground state energy per bond Eb=0.179603(J=1)and magnetization M=0.238697 of the system.By comparison,its magnetization is about 48%larger than our numerical results,because the linear spin-wave theory ignores the quantum fluctuations of the system in its calculations.As the semi-classical analysis algorithm,spin wave theory plays a pioneering role in quantum magnetism.Mastering this method is very helpful for future works.