Classifying spin liquid states on kagome Heisenberg model by symmetric projected entangled simplex states

Guan-Lin Lin^1*, Shenghan Jiang^3,4, Ying-Jer Kao^1,2

¹Department of Physics and Center for Theoretical Physics, National Taiwan University, Taipei, Taiwan
²Physics Division, National Center for Theoretical Science, Taipei, Taiwan
³Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing, China
⁴Department of Physics and Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California, USA

* Presenter:Guan-Lin Lin, email:klwalt861206@gmail.com

One of the central goal in condensed matter physics is accurately generating quantum phase diagrams of realistic interacting systems. The study of quantum many-body entanglement has provided many key insights into the structure of quantum states of matter. Tensor networks (TN) have recently emerged as powerful numerical techniques that reliably capture the entanglement structure and quantum correlations in the system, offering the natural language to describe quantum states. The ground state of spin-1/2 kagome antiferromagnetic Heisenberg (KAFH) model shows strong evidence of a spin liquid phase by recent numerical studies; however, the features of this new exotic phase of matter all still unknown.
We utilize symmetric projected entangled simplex states (PESS) to classify possible Z2 spin liquid phases and numerically obtain the optimal ground state. In particular, we employ the concept of projective symmetry group (PSG) for PESS, allowing us to deal with tensor gauge equivalence beforehand in order to classify our local tensor in the TN wavefunction. The classification allows us to obtain a finite number of classes of symmetric PESS wavefunctions, and perform a variational simple update simulation within each class separately. Additionally, we use the Corner Transfer Matrix Renormalization Group (CTMRG) algorithm to obtain more accurate energy measurement. Therefore, our approach enables us to understand the nature of the ground state of KAFH model in the thermodynamic limit. Furthermore, the minimal entanglement states (MES) overlapping and the VUMPS method provide evidence of the Z2 topological order within our ground state wavefunction.

Keywords: strongly correlated system, spin liquid, topological order, tensor network