Optimized Decimation of Tensor Networks with Super-orthogonalization for Two-Dimensional Quantum Lattice Models

TL;DR

This paper introduces an innovative tensor network decimation algorithm with super-orthogonalization that efficiently computes thermodynamic and ground state properties of 2D quantum lattice models, including frustrated systems.

Contribution

The paper presents a new tensor network algorithm that transforms 2D quantum models into a 3D tensor network and uses Tucker decomposition for optimal approximation, improving efficiency and accuracy.

Findings

Comparable accuracy to quantum Monte Carlo methods

Effective for frustrated quantum spin models

First application of Tucker decomposition in this context

Abstract

A novel algorithm based on the optimized decimation of tensor networks with super-orthogonalization (ODTNS) that can be applied to simulate efficiently and accurately not only the thermodynamic but also the ground state properties of two-dimensional (2D) quantum lattice models is proposed. By transforming the 2D quantum model into a three-dimensional (3D) closed tensor network (TN) comprised of the tensor product density operator and a 3D brick-wall TN, the free energy of the system can be calculated with the imaginary time evolution, in which the network Tucker decomposition is suggested for the first time to obtain the optimal lower-dimensional approximation on the bond space by transforming the TN into a super-orthogonal form. The efficiency and accuracy of this algorithm are testified, which are fairly comparable with the quantum Monte Carlo calculations. Besides, the present ODTNS scheme can also be applicable to the 2D frustrated quantum spin models with nice efficiency.