Tao Xiang (Institute of Physics, Chinese Academy of Sciences, Beijing, China)

Renormalization of quantum many-body systems by the projected entangled simplex states

We propose a new class of tensor networkstates, named as projected entangled simplex states (PESS), for studying ground state properties of quantum lattice models. It extends the pair correlation in the projected entangled pair states (PEPS) to a simplex. The PESS is an exact repre-sentation of the so-called simplex solid states and an efficient trial wavefunction that satisfies the area law of entanglement entropy. We introduce a simple update renormalization method for evaluating the PESS wavefunction based on the higher order singular value decom-position of tensors under the framework of imaginary time evolution. By applying it to the spin-1/2 Heisenberg model on the Kagome lattice, we obtain an accurate result for the ground state energy, which agrees with other numerical calculations and sets a new upper bound for the ground state energy.

Reference:
Z. Y. Xie, J. Chen, J. F. Yu, X. Kong, B. Normand, and T. Xiang, Phys. Rev. X 4, 011025 (2014)