Theory of network contractor dynamics for exploring thermodynamic properties of two-dimensional quantum lattice models

Abstract

Based on the tensor network state representation, we develop a nonlinear dynamic theory, coined network contractor dynamics (NCD), to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-1 decomposition in the multilinear algebra, the NCD scheme makes the contraction of the tensor network of the partition function be realized through a contraction of a local tensor cluster with vectors on its boundary. An imaginary-time-sweep algorithm for implementation of the NCD method is proposed for practical numerical simulations. We benchmark the NCD scheme on the square Ising model, which shows great accuracy. Also, the results on the spin-1/2 Heisenberg antiferromagnet on a honeycomb lattice are disclosed to be in good agreement with the quantum Monte Carlo calculations. The quasientanglement entropy $S$, Lyapunov exponent ${I}^{\text{Lya}}$, and loop character ${I}^{\text{loop}}$ are introduced within the dynamic scheme, which are found to display ``nonlocality'' near the critical point, and can be applied to determine the thermodynamic phase transitions of both classical and quantum systems.