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

The spin-1/2 kagome Heisenberg antiferromagnet is one of the most promising candidate systems for a quantum spin liquid. However, the precise nature of its ground state is still being debated. Recent density-matrix renormalization group (DMRG) calculations show evidence for a possible $Z_2$ spin-liquid phase, the effective description of which is a $Z_2$ gauge theory [1,2]. In this work, we construct a minimal $Z_2$ gauge Hamiltonian encapsulating the DMRG phenomenology in the $S=0$ sector. We generalize Misguich's Hamiltonian [3] by including dynamical visons [4]. We show that our minimal model naturally produces the diamond resonance pattern observed in DMRG. Moreover, puzzling even-odd effects in kagome cylinders are easily explained by our model. We also predict the existence of edge spinons in certain cylindrical geometries.\\[4pt] [1] S. Yan, D. A. Huse, and S. R. White, Science \textbf{332}, 1173 (2011).\\[0pt] [2] S. Depenbrock, I. P. McCulloch, and U. Schollw\"ock, Phys. Rev. Lett. \textbf{109}, 067201 (2012).\\[0pt] [3] G. Misguich, D. Serban, and V. Pasquier, Phys. Rev. Lett. \textbf{89}, 137202 (2002).\\[0pt] [4] Y. Huh, M. Punk, and S. Sachdev, Phys. Rev. B \textbf{84}, 094419 (2011).