Cheng Peng¹ , Shi-Ju Ran^2,3,a , Maciej Lewenstein^3,4 , and Gang Su^1,5,b

¹ Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, P.R. China

² Department of Physics, Capital Normal University, Beijing 100048, P.R. China

³ ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860 Castelldefels, Barcelona, Spain

⁴ ICREA, Pg. Llu´ıs Companys 23, 08010 Barcelona, Spain

⁵ Kavli Institute for Theoretical Sciences, CAS Center for Excellence in Topological Quantum Computation, University of Chinese Academy of Sciences, Beijing 100190, P.R. China

The scaling behaviors of entanglement entropy (EE) against dimension cut-off of density matrix renormalization group (DMRG) in an anisotropic Heisenberg model on honeycomb lattice are investigated. In the gapped dimer phase, the entanglement spectrum (ES) exhibits large gaps and the EE shows an unexpected linear scaling before convergence. In contrast in the gapless N´eel phase, the ES decays in a much smoother way, and the EE scales logarithmically. Our calculations show that the linear scaling in the dimer phase originates from one dominant Schmidt number plus n (nearly) degenerate Schmidt numbers that are much smaller than the dominant one. The non-trivial entanglement-scaling properties of the dimer and N´eel phases could potentially be used for their detections.