A Phenomenological Theory for the $Z_2$ Spin-Liquid Phase of the $S=1/2$ Kagome Heisenberg Antiferromagnet

Xi Chen, Shi-Ju Ran, Tao Liu +3 more

Federico Becca, Yasir Iqbal, Didier Poilblanc

Yuan Wan, Oleg Tchernyshyov

We construct a phenomenological ${Z}_{2}$ lattice gauge theory to describe the spin-liquid state of the $S=\frac{1}{2}$ kagome Heisenberg antiferromagnet in the sector with zero total spin. The model is a natural generalization of the Misguich-Serban-Pasquier Hamiltonian with added interactions that are strongly constrained by lattice symmetries. We are able to reproduce qualitatively many of the characteristic features observed in recent numerical studies. We also make connections to the previous works along similar lines.

Shenghan Jiang, Panjin Kim, Jung Hoon Han +1 more

The properties of ground state of spin- \frac{1}{2} 1 2 kagome antiferromagnetic Heisenberg (KAFH) model have attracted considerable interest in the past few decades, and recent numerical simulations reported a spin liquid phase. The nature of the spin liquid phase remains unclear. For instance, the interplay between symmetries and Z_2 Z 2 topological order leads to different types of Z_2 Z 2 spin liquid phases. In this paper, we develop a numerical simulation method based on symmetric projected entangled-pair states (PEPS), which is generally applicable to strongly correlated model systems in two spatial dimensions. We then apply this method to study the nature of the ground state of the KAFH model. Our results are consistent with that the ground state is a U(1) U ( 1 ) Dirac spin liquid rather than a Z_2 Z 2 spin liquid.

Dong-Ning Sheng, Wei Kang Zhu, Shou-Shu Gong

Yin-Chen He, Yan Chen

By using the density matrix renormalization group, we study the spin-liquid phases of spin-$1/2$ XXZ kagome antiferromagnets. We find that the emergence of spin liquid phase does not depend on the anisotropy of the XXZ interaction. In particular, the two extreme limits---Ising (strong $S^z$ interaction) and XY (zero $S^z$ interaction)---host the same spin-liquid phases as the isotropic Heisenberg model. Both the time-reversal-invariant spin liquid and the chiral spin liquid with spontaneous time-reversal symmetry breaking are obtained. We show they evolve continuously into each other by tuning the second- and third-neighbor interactions. To understand the continuous phase transition between these two spin liquids, we construct a phenomenological theory, and propose the double-semion spin liquid as the candidate ground state of nearest-neighbor XXZ kagome antiferromagnets, including the most studied nearest-neighbor spin-$1/2$ kagome antiferromagnetic Heisenberg model.