Modified Tucker Decomposition for Tensor Network and Fast Linearized Tensor Renormalization Group Algorithm for Two-Dimensional Quantum Spin Lattice Systems

TL;DR

This paper introduces a novel fast linearized tensor renormalization group algorithm with a modified Tucker decomposition, enabling efficient and accurate analysis of ground states and thermodynamics in 2D quantum spin systems.

Contribution

It presents a new algorithm combining modified Tucker decomposition with tensor networks for improved simulation of 2D quantum lattice systems.

Findings

Accurately computed ground states and thermodynamics of 2D quantum spin systems.

Identified quantum phase transition from antiferromagnetic to spin liquid phase.

Results agree well with quantum Monte Carlo simulations.

Abstract

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.