  We propose a novel algorithm with a modified Tucker decomposition for tensor
network that allows for efficiently and precisely calculating the ground state
and thermodynamic properties of two-dimensional (2D) quantum spin lattice
systems, and is coined as the fast linearized tensor renormalization group
(fLTRG). Its amazing efficiency and precision are examined by studying the
spin-1/2 anisotropic Heisenberg antiferromagnet on a honeycomb lattice, and the
results are found to be fairly in agreement with the quantum Monte Carlo
calculations. It is also successfully applied to tackle a quasi-2D spin-1/2
frustrated bilayer honeycomb Heisenberg model, where a quantum phase transition
from an ordered antiferromagnetic state to a gapless quantum spin liquid phase
is found. The thermodynamic behaviors of this frustrated spin system are also
explored. The present fLTRG algorithm could be readily extended to other
quantum lattice systems.
