Theory of Network Contractor Dynamics for Exploring Thermodynamic Properties of Two-dimensional Quantum Lattice Models

TL;DR

This paper introduces a nonlinear dynamic tensor network method called network contractor dynamics (NCD) to efficiently compute thermodynamic properties of 2D quantum lattice models, demonstrating high accuracy and new insights into phase transitions.

Contribution

The paper develops the NCD scheme using rank-1 tensor decomposition and an imaginary-time-sweep algorithm, providing a novel approach for simulating 2D quantum systems.

Findings

NCD accurately reproduces results for the square Ising model.

NCD's results for the honeycomb Heisenberg model agree with quantum Monte Carlo.

Dynamic quantities like entropy and Lyapunov exponent reveal nonlocality near critical points.

Abstract

Based on the tensor network state representation, we develop a nonlinear dynamic theory coined as network contractor dynamics (NCD) to explore the thermodynamic properties of two-dimensional quantum lattice models. By invoking the rank-$1$ decomposition in the multi-linear 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 a great accuracy. Besides, the results on the spin-1/2 Heisenberg antiferromagnet on honeycomb lattice are disclosed in good agreement with the quantum Monte Carlo calculations. The quasi-entanglement entropy $S$, Lyapunov exponent $I^{lya}$ and loop character $I^{loop}$ are introduced within the dynamic scheme, which are found to display the ``nonlocality" near the critical point, and can be applied to determine the thermodynamic phase transitions of both classical and quantum systems.